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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1998-05-11T05:39:17 | 9708 | alg-geom/9708002 | en | https://arxiv.org/abs/alg-geom/9708002 | [
"alg-geom",
"math.AG"
] | alg-geom/9708002 | James A. Carlson | James A. Carlson and Domingo Toledo | Discriminant Complements and Kernels of Monodromy Representations | 20 page dvi file available at
http://www.math.utah.edu/~carlson/eprints.html Minor changes for final
version to appear in Duke J. Math | null | null | null | null | We show that the kernel of the monodromy representation for hypersurfaces of
degree d and dimension n is large for d at least three with the exception of
the cases (d,n) = (3,0) and (3,1). For these the kernel is finite. By "large"
we mean a group that admits a homomorphism to a semisimple Lie group of
noncompact typ... | [
{
"version": "v1",
"created": "Fri, 1 Aug 1997 23:18:27 GMT"
},
{
"version": "v2",
"created": "Fri, 13 Feb 1998 16:48:02 GMT"
},
{
"version": "v3",
"created": "Mon, 11 May 1998 03:39:15 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Carlson",
"James A.",
""
],
[
"Toledo",
"Domingo",
""
]
] | alg-geom | \section{Introduction}
\secref{introsection}
A hypersurface of degree $d$ in a complex projective space
$\P^{n+1}$ is defined by an equation of the form
$$
F(x) = \sum a_L x^L = 0,
\eqn
\eqref{universalhypersurface}
$$
where $x^L = x_0^{L_0} \cdots x_{n+1}^{L_{n+1}}$ is a monomial of degree
$d$ and where t... |
1997-08-14T10:59:42 | 9708 | alg-geom/9708012 | en | https://arxiv.org/abs/alg-geom/9708012 | [
"alg-geom",
"math.AG"
] | alg-geom/9708012 | Lothar Goettsche | Barbara Fantechi, Lothar G\"ottsche, Duco van Straten | Euler number of the compactified Jacobian and multiplicity of rational
curves | LaTeX, 16 pages with 1 figure | null | null | null | null | We show that the Euler number of the compactified Jacobian of a rational
curve $C$ with locally planar singularities is equal to the multiplicity of the
$\delta$-constant stratum in the base of a semi-universal deformation of $C$.
In particular, the multiplicity assigned by Yau, Zaslow and Beauville to a
rational cur... | [
{
"version": "v1",
"created": "Thu, 14 Aug 1997 08:59:50 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Fantechi",
"Barbara",
""
],
[
"Göttsche",
"Lothar",
""
],
[
"van Straten",
"Duco",
""
]
] | alg-geom | \section{Introduction}
Let $C$ be a reduced and irreducible projective curve with singular set
$\Sigma \subset C$ and let $n: \widetilde{C} \longrightarrow C$ be
its normalisation. The generalised Jacobian $JC$ of $C$ is an extension of
$J\widetilde{C}$ by an affine commutative group of dimension
$$\delta:=\dim H^0(n_... |
1997-12-16T01:08:53 | 9708 | alg-geom/9708007 | en | https://arxiv.org/abs/alg-geom/9708007 | [
"alg-geom",
"math.AG"
] | alg-geom/9708007 | Yuri G. Zarhin | Yuri G. Zarhin | Torsion of abelian varieties, Weil classes and cyclotomic extensions | LaTeX 2e 17 pages | null | null | null | null | Let $K$ be a field finitely generated over the field of rational numbers,
$K(c)$ the extension of $K$ obtained by adjoining all roots of unity, $L$ an
infinite Galois extension of $K$, $X$ an abelian variety defined over $K$. We
prove that under certain conditions on $X$ and $K$ the existence of infinitely
many L-rat... | [
{
"version": "v1",
"created": "Mon, 4 Aug 1997 23:46:42 GMT"
},
{
"version": "v2",
"created": "Wed, 27 Aug 1997 19:17:28 GMT"
},
{
"version": "v3",
"created": "Wed, 3 Sep 1997 15:12:11 GMT"
},
{
"version": "v4",
"created": "Tue, 9 Sep 1997 16:53:41 GMT"
},
{
"vers... | 2008-02-03T00:00:00 | [
[
"Zarhin",
"Yuri G.",
""
]
] | alg-geom | \section{Main construction}
Let $F$ be the center of $\mathrm{End}_K(X)\otimes{\mathbf Q}$, $R_F=F\bigcap \mathrm{End}_K(X)$ the center of $\mathrm{End}_K(X)$. We put
$$V_{{\mathbf Z}}=V_{{\mathbf Z}}(X)=H_1(X({\mathbf C}),{\mathbf Z}), \quad V=V(X)=H_1(X({\mathbf C}),{\mathbf Q})= V_{{\mathbf Z}}\otimes{\mathbf Q}.... |
1997-08-22T16:19:27 | 9708 | alg-geom/9708020 | en | https://arxiv.org/abs/alg-geom/9708020 | [
"alg-geom",
"math.AC",
"math.AG"
] | alg-geom/9708020 | Gunnar Floystad | Gunnar Floystad | A property deducible from the generic initial ideal | Completely revised compared to earlier hardcopy versions. AMS-Latex
v1.2, 13 pages | Journal of Pure and Applied Algebra, 136 (1999), no.2, p.127-140 | 10.1016/S0022-4049(97)00165-5 | null | null | Let $S_d$ be the vector space of monomials of degree $d$ in the variables
$x_1, ..., x_s$. For a subspace $V \sus S_d$ which is in general coordinates,
consider the subspace $\gin V \sus S_d$ generated by initial monomials of
polynomials in $V$ for the revlex order. We address the question of what
properties of $V$ m... | [
{
"version": "v1",
"created": "Fri, 22 Aug 1997 14:19:15 GMT"
}
] | 2011-12-14T00:00:00 | [
[
"Floystad",
"Gunnar",
""
]
] | alg-geom | \section*{Introduction}
During the recent years the generic initial ideal of a homogeneous ideal
has attracted some attention as an invariant.
An intriguing problem is what algebraic or geometric properties of the
original ideal can be deduced from the generic initial ideal.
In this paper we take perhaps the most el... |
1997-08-22T10:49:15 | 9708 | alg-geom/9708019 | en | https://arxiv.org/abs/alg-geom/9708019 | [
"alg-geom",
"math.AG"
] | alg-geom/9708019 | Alexander A. Voronov | Alexander A. Voronov (RIMS and M.I.T.) | Stability of the Rational Homotopy Type of Moduli Spaces | 7 pages, 1 figure | null | null | RIMS-1157 | null | We show that for g > 2k+2 the k-rational homotopy type of the moduli space
M_{g,n} of algebraic curves of genus g with n punctures is independent of g,
and the space M_{g,n} is k-formal. This implies the existence of a limiting
rational homotopy type of M_{g,n} as g goes to infinity and the formality of
it.
| [
{
"version": "v1",
"created": "Fri, 22 Aug 1997 08:49:13 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Voronov",
"Alexander A.",
"",
"RIMS and M.I.T."
]
] | alg-geom | \section*{Introduction}
The description of the algebraic topology of the moduli space
$\mgn{g}$ of compact complex algebraic curves has long been a
tantalizing problem. The idea of ``stable cohomology '' of $\mgn{g}$ as the
genus $g \to \infty$, brought in by J.~L. Harer and D.~Mumford,
suggested a more graspable obj... |
1997-08-07T16:22:05 | 9708 | alg-geom/9708010 | en | https://arxiv.org/abs/alg-geom/9708010 | [
"alg-geom",
"math.AG",
"math.QA",
"q-alg"
] | alg-geom/9708010 | Carlos Simpson | Carlos Simpson (CNRS, Universit\'e Paul Sabatier, Toulouse, France) | Limits in $n$-categories | Approximately 90 pages | null | null | null | null | We define notions of direct and inverse limits in an $n$-category. We prove
that the $n+1$-category $nCAT'$ of fibrant $n$-categories admits direct and
inverse limits. At the end we speculate (without proofs) on some applications
of the notion of limit, including homotopy fiber product and homotopy coproduct
for $n$-... | [
{
"version": "v1",
"created": "Thu, 7 Aug 1997 16:31:55 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Simpson",
"Carlos",
"",
"CNRS, Université Paul Sabatier, Toulouse, France"
]
] | alg-geom | \section*{Limits in $n$-categories}
Carlos Simpson\newline
CNRS, UMR 5580, Universit\'e Paul Sabatier, 31062 Toulouse CEDEX, France.
\bigskip
\numero{Introduction}
One of the main notions in category theory is the notion of limit. Similarly,
one of the most commonly used techniques in homotopy theory is the notion... |
1997-08-18T09:52:59 | 9708 | alg-geom/9708014 | en | https://arxiv.org/abs/alg-geom/9708014 | [
"alg-geom",
"math.AG"
] | alg-geom/9708014 | Leticia B. Paz | L. Brambila-Paz and H. Lange | A stratification of the moduli space of vector bundles on curves | Latex, Permanent e-mail L. Brambila-Paz: lebp@xanum.uam.mx
Classification: 14D, 14F | null | null | null | null | Let $E$ be a vector bundle of rank $r\geq 2$ on a smooth projective curve $C$
of genus $g \geq 2$ over an algebraically closed field $K$ of arbitrary
characteristic. For any integer with $1\le k\le r-1$ we define
$${\se}_k(E):=k\deg E-r\max\deg F.$$ where the maximum is taken over all
subbundles $F$ of rank $k$ of $E... | [
{
"version": "v1",
"created": "Mon, 18 Aug 1997 07:52:26 GMT"
}
] | 2016-08-30T00:00:00 | [
[
"Brambila-Paz",
"L.",
""
],
[
"Lange",
"H.",
""
]
] | alg-geom | \section{The invariants ${ {}{\mbox{\euf s}_k}}(E)$}
Let $C$ be a smooth projective curve of genus $g\ge 2$ over an
algebraically closed field $K$ of arbitrary characteristic. and let $E$
denote a vector bundle of rank $r\ge 2$ over $C$. For any integer $k$ with
$1\le k\le r-1$ let ${}{Sb_k}(E)$ denote the {\it set ... |
1998-08-05T18:28:10 | 9708 | alg-geom/9708011 | en | https://arxiv.org/abs/alg-geom/9708011 | [
"alg-geom",
"math.AG"
] | alg-geom/9708011 | Balazs Szendroi | Balazs Szendroi | Some finiteness results for Calabi-Yau threefolds | 15 pages LaTex, uses amstex, amscd. New title, paper completely
rewritten, results same as in previous versions | null | null | null | null | We investigate the moduli theory of Calabi--Yau threefolds, and using
Griffiths' work on the period map, we derive some finiteness results. In
particular, we confirm a prediction of Morrison's Cone Conjecture.
| [
{
"version": "v1",
"created": "Tue, 12 Aug 1997 15:15:06 GMT"
},
{
"version": "v2",
"created": "Wed, 29 Oct 1997 11:38:37 GMT"
},
{
"version": "v3",
"created": "Wed, 5 Aug 1998 16:28:09 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Szendroi",
"Balazs",
""
]
] | alg-geom | \section*{Introduction}
If $X$ is a smooth complex projective $n$-fold,
Hodge--Lefschetz theory provides
a filtration on the primitive cohomology $H^n_0(X,{\mathbb C})$ by complex
subspaces, satisfying certain compatibility conditions with a bilinear
form $Q$ on cohomology. This gives a map called the
{\it period ma... |
1997-08-26T19:03:35 | 9708 | alg-geom/9708022 | en | https://arxiv.org/abs/alg-geom/9708022 | [
"alg-geom",
"math.AC",
"math.AG"
] | alg-geom/9708022 | Uwe Nagel | J. C. Migliore, U. Nagel, C. Peterson | Buchsbaum-Rim sheaves and their multiple sections | 27 pages, AMS-LaTeX | null | null | null | null | This paper begins by introducing and characterizing Buchsbaum-Rim sheaves on
$Z = \Proj R$ where $R$ is a graded Gorenstein K-algebra. They are reflexive
sheaves arising as the sheafification of kernels of sufficiently general maps
between free R-modules. Then we study multiple sections of a Buchsbaum-Rim
sheaf $\cBf... | [
{
"version": "v1",
"created": "Tue, 26 Aug 1997 17:03:21 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Migliore",
"J. C.",
""
],
[
"Nagel",
"U.",
""
],
[
"Peterson",
"C.",
""
]
] | alg-geom | \section{Introduction}
A fundamental method for constructing algebraic varieties is to
consider the degeneracy locus of a morphism between a pair of coherent
sheaves. By varying
the morphism one obtains families of varieties. By placing various
restrictions on the
coherent sheaves one can force the degeneracy locus to... |
2005-11-19T08:38:21 | 9708 | alg-geom/9708006 | en | https://arxiv.org/abs/alg-geom/9708006 | [
"alg-geom",
"math.AC",
"math.AG"
] | alg-geom/9708006 | Joseph Lipman | Leovigildo Alonso, Ana Jeremias, Joseph Lipman | Duality and flat base change on formal schemes | 89 pages. Change from published version: in section 2.5, about
dualizing complexes on formal schemes, a weakening of one flawed Lemma is
proved, and shown adequate for the several applications made of the original.
For another correction, see math.AG/0106239 | Contemporary Math. 244 (1999), 3-90 | null | null | null | We give several related versions of global Grothendieck Duality for unbounded
complexes on noetherian formal schemes. The proofs, based on a non-trivial
adaptation of Deligne's method for the special case of ordinary schemes, are
reasonably self-contained, modulo the Special Adjoint Functor Theorem. An
alternative ap... | [
{
"version": "v1",
"created": "Mon, 4 Aug 1997 17:48:14 GMT"
},
{
"version": "v2",
"created": "Wed, 14 Oct 1998 18:40:15 GMT"
},
{
"version": "v3",
"created": "Sat, 19 Nov 2005 07:38:21 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Alonso",
"Leovigildo",
""
],
[
"Jeremias",
"Ana",
""
],
[
"Lipman",
"Joseph",
""
]
] | alg-geom | \section{Preliminaries and main theorems.}
\label{S:prelim}
First we need some notation and terminology. Let $X$ be a ringed
space,\index{ringed space} i.e., a topological space together with a sheaf of
commutative rings ${\mathcal O}_{\<\<X}$.%
\index{ ${\mathbf R}$@${\mathcal O}_{\<\<\<X}$ (structure sheaf of ringe... |
1998-01-30T16:29:59 | 9708 | alg-geom/9708016 | en | https://arxiv.org/abs/alg-geom/9708016 | [
"alg-geom",
"math.AG"
] | alg-geom/9708016 | Nhadhule | Klaus Hulek | Nef Divisors on Moduli Spaces of Abelian Varieties | LaTeX2e, 23 pages. The proof of the main result has been shortened.
In particular, the former technical propositions 4.3 and 4.4 were replaced by
a simpler argument | null | null | null | null | We determine the cone of nef divisors on the Voronoi compactification A_g^*
of the moduli space A_g of principally polarized abelian varieties of dimension
g for genus g=2,3. As a corollary we obtain that the spaces A_g^*(n) with
level-n structure are a minimal, resp. canonical, model for g=2, n>=4, resp.
n>=5 and g=... | [
{
"version": "v1",
"created": "Tue, 19 Aug 1997 12:24:04 GMT"
},
{
"version": "v2",
"created": "Fri, 30 Jan 1998 15:29:58 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Hulek",
"Klaus",
""
]
] | alg-geom | \section{Introduction}
Let ${\cal A}_g$ be the moduli space of principally polarized abelian varieties
of dimension $g$. Over the complex numbers ${\cal A}_g={\mathbb{H}}_g/\Gamma_g$ where
${\mathbb{H}}_g$ is the Siegel space of genus $g$ and $\Gamma_g=\on{Sp}(2g,{\mathbb{Z}})$. We
denote the torodial compactification... |
1997-08-26T18:18:51 | 9708 | alg-geom/9708021 | en | https://arxiv.org/abs/alg-geom/9708021 | [
"alg-geom",
"math.AC",
"math.AG"
] | alg-geom/9708021 | Uwe Nagel | M. Kreuzer, J. C. Migliore, U. Nagel, C. Peterson | Determinantal schemes and Buchsbaum-Rim sheaves | 20 pages, LaTeX | null | null | null | null | Let $\phi$ be a generically surjective morphism between direct sums of line
bundles on $\proj{n}$ and assume that the degeneracy locus, $X$, of $\phi$ has
the expected codimension. We call $B_{\phi} = \ker \phi$ a (first)
Buchsbaum-Rim sheaf and we call $X$ a standard determinantal scheme. Viewing
$\phi$ as a matrix ... | [
{
"version": "v1",
"created": "Tue, 26 Aug 1997 16:18:20 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Kreuzer",
"M.",
""
],
[
"Migliore",
"J. C.",
""
],
[
"Nagel",
"U.",
""
],
[
"Peterson",
"C.",
""
]
] | alg-geom | \section{Introduction}
A natural and efficient method for producing numerous examples of interesting
schemes is to consider the vanishing locus of the minors of a homogeneous
polynomial matrix. If the matrix satisfies certain genericity conditions then
the resulting schemes have a number of well described properties. ... |
1997-08-29T22:11:12 | 9708 | alg-geom/9708026 | en | https://arxiv.org/abs/alg-geom/9708026 | [
"alg-geom",
"math.AG"
] | alg-geom/9708026 | Frank Sottile | Frank Sottile (University of Toronto) | Pieri-type formulas for maximal isotropic Grassmannians via triple
intersections | LaTeX 2e, 24 pages (9 pages is an appendix detailing the proof in the
symplectic case). Expanded version of MSRI preprint 1997-062 | Colloquium Mathematicum, Vol. 82 (1999), 49--63. | null | null | null | We give an elementary proof of the Pieri-type formula in the cohomology of a
Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic
vector space. This proof proceeds by explicitly computing a triple intersection
of Schubert varieties. The decisive step is an explicit description of the
interse... | [
{
"version": "v1",
"created": "Fri, 29 Aug 1997 20:10:43 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Sottile",
"Frank",
"",
"University of Toronto"
]
] | alg-geom | \section*{Introduction}
The goal of this paper is to give an elementary geometric proof of
Pieri-type formulas in the cohomology of
Grassmannians of maximal isotropic subspaces of odd orthogonal or symplectic
vector spaces.
For this, we explicitly compute a triple intersection of
Schubert varieties, where one is a spe... |
1998-11-25T06:12:16 | 9708 | alg-geom/9708004 | en | https://arxiv.org/abs/alg-geom/9708004 | [
"alg-geom",
"math.AG"
] | alg-geom/9708004 | Mark De Cataldo | Mark Andrea A. de Cataldo | Effective nonvanishing, effective global generation | LaTex (article) 13 pages; revised: one section added; to appear in
Ann. Inst. Fourier | null | null | null | null | We prove a multiple-points higher-jets nonvanishing theorem by the use of
local Seshadri constants. Applications are given to effectivity problems such
as constructing rational and birational maps into Grassmannians, and the global
generation of vector bundles.
| [
{
"version": "v1",
"created": "Sat, 2 Aug 1997 01:50:03 GMT"
},
{
"version": "v2",
"created": "Wed, 25 Nov 1998 05:12:29 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"de Cataldo",
"Mark Andrea A.",
""
]
] | alg-geom | \section{Introduction}
\label{intr}
Koll\'ar's nonvanishing
theorem \ci{koebpf}, 3.2 is an instrument to make
Kawamata-Shokurov base-point-freeness assertion into an effective one.
His result can be applied to a variety of other situations;
see \ci{koebpf}, \S4, \ci{koshafinv}, \S8 and \ci{koshaf}, \S14.
The basic ... |
1997-08-29T11:25:45 | 9708 | alg-geom/9708025 | en | https://arxiv.org/abs/alg-geom/9708025 | [
"alg-geom",
"math.AG"
] | alg-geom/9708025 | Georg Hein | Georg Hein | Duality Construction of Moduli Spaces | 12 pages LaTeX using pb-diagram.sty | null | null | null | null | We show for the moduli space of rank-2 coherent sheaves on an algebraic
surface that there exists a 'dual' moduli space. This dual space allows a
construction of the first one without using the GIT construction. Furthermore,
we obtain a Barth-morphism, generalizing the concept of jumping lines. This
morphism is by co... | [
{
"version": "v1",
"created": "Fri, 29 Aug 1997 09:25:28 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Hein",
"Georg",
""
]
] | alg-geom | \section*{Introduction}
In \S 1 of Faltings' article \cite{Fal} a ``GIT-free'' construction
is given for the moduli spaces of vector bundles on curves using
generalized theta functions.
Incidentally, this construction is implicitly described
in Le Potier's article \cite{LP2}.
The aim of this paper is to generalize the
... |
1998-11-25T06:04:39 | 9708 | alg-geom/9708003 | en | https://arxiv.org/abs/alg-geom/9708003 | [
"alg-geom",
"math.AG"
] | alg-geom/9708003 | Mark De Cataldo | Mark Andrea A. de Cataldo | Singular hermitian metrics on vector bundles | LaTex (article) 25 pages; revised: minor changes; to appear in
Crelle's J; dedicated to Michael Schneider | null | null | null | null | We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic
vector bundles and define positivity in view of $L^2$-estimates. Associated
with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a
certain $d''$-complex. We prove a vanishing theorem for the cohomology of this
sheaf. Al... | [
{
"version": "v1",
"created": "Sat, 2 Aug 1997 01:32:14 GMT"
},
{
"version": "v2",
"created": "Wed, 25 Nov 1998 05:05:36 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"de Cataldo",
"Mark Andrea A.",
""
]
] | alg-geom | \section{Introduction}
In this study I introduce a notion of singular hermitian metrics
({\em s.h.m.}) on holomorphic vector bundles over complex manifolds.
The original motivation was to explore the possibility of employing,
in the setting of vector bundles,
the new transcendental techniques developed by Demailly and... |
1997-09-04T21:02:01 | 9708 | alg-geom/9708001 | en | https://arxiv.org/abs/alg-geom/9708001 | [
"alg-geom",
"math.AG"
] | alg-geom/9708001 | Rahul Pandharipande | T. Graber and R. Pandharipande | Localization of virtual classes | 29 pages, LaTeX2e, General revision including error corrections | null | null | null | null | We prove a localization formula for virtual fundamental classes in the
context of torus equivariant perfect obstruction theories. As an application,
the higher genus Gromov-Witten invariants of projective space are expressed as
graph sums of tautological integrals over moduli spaces of stable pointed
curves (generali... | [
{
"version": "v1",
"created": "Fri, 1 Aug 1997 21:03:40 GMT"
},
{
"version": "v2",
"created": "Thu, 4 Sep 1997 19:01:26 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Graber",
"T.",
""
],
[
"Pandharipande",
"R.",
""
]
] | alg-geom | \section{\bf{Introduction}}
We prove a localization formula for the
virtual fundamental class in the general context of
$\mathbb{C}^*$-equivariant perfect obstruction theories.
Let $X$ be an algebraic scheme with a $\mathbb{C}^*$-action
and a $\mathbb{C}^*$-equivariant perfect obstruction theory.
The virtual fundament... |
1998-04-03T02:11:23 | 9702 | alg-geom/9702015 | en | https://arxiv.org/abs/alg-geom/9702015 | [
"alg-geom",
"math.AG"
] | alg-geom/9702015 | Rick Miranda | C. Ciliberto (U. of Rome II), R. Miranda (Colorado State U.) | Degenerations of Planar Linear Systems | material is streamlined and some is moved to a forthcoming paper | null | null | null | null | Fixing $n$ general points $p_i$ in the plane, what is the dimension of the
space of plane curves of degree $d$ having multiplicity $m_i$ at $p_i$ for each
$i$? In this article we propose an approach to attack this problem, and
demonstrate it by successfully computing this dimension for all $n$ and for
$m_i$ constant,... | [
{
"version": "v1",
"created": "Fri, 21 Feb 1997 20:37:02 GMT"
},
{
"version": "v2",
"created": "Fri, 3 Apr 1998 00:11:22 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Ciliberto",
"C.",
"",
"U. of Rome II"
],
[
"Miranda",
"R.",
"",
"Colorado State U."
]
] | alg-geom | \section*{Introduction}
Fix the projective plane ${\mathbb{P}}^2$
and $n+1$ general points $p_0, p_1, \ldots, p_n$ in it.
Let $H$ denote the line class of the plane.
Consider the linear system consisting of
plane curves of degree $d$ (that is, divisors in $|dH|$)
with multiplicity $m_0$ at $p_0$
and multiplicity $m_i$ ... |
1997-02-20T16:46:35 | 9702 | alg-geom/9702013 | en | https://arxiv.org/abs/alg-geom/9702013 | [
"alg-geom",
"math.AG"
] | alg-geom/9702013 | Gian Mario Besana | Alberto Alzati, Marina Bertolini, Gian Mario Besana | Numerical Criteria for vey Ampleness of Divisors on Projective Bundles
over an elliptic curve | AMS-Latex, 18 pages, Canadian Journal of Math, Dec 1996 | null | null | null | null | In Butler, J.Differential Geom. 39 (1):1--34,1994, the author gives a
sufficient condition for a line bundle associated with a divisor D to be
normally generated on $X=P(E)$ where E is a vector bundle over a smooth curve
C. A line bundle which is ample and normally generated is automatically very
ample. Therefore the... | [
{
"version": "v1",
"created": "Thu, 20 Feb 1997 15:48:41 GMT"
}
] | 2019-08-17T00:00:00 | [
[
"Alzati",
"Alberto",
""
],
[
"Bertolini",
"Marina",
""
],
[
"Besana",
"Gian Mario",
""
]
] | alg-geom | \section{Introduction}
Ampleness of divisors on algebraic varieties is a numerical property. On
the
other hand it is in general very difficult to give numerical necessary and
sufficient
conditions for the very ampleness of divisors. In \cite{bu} the author
gives a
sufficient condition for a line bundle associated with... |
1997-02-14T20:33:23 | 9702 | alg-geom/9702010 | en | https://arxiv.org/abs/alg-geom/9702010 | [
"alg-geom",
"math.AG"
] | alg-geom/9702010 | Michael Finkelberg | Michael Finkelberg and Alexander Kuznetsov (Independent University of
Moscow) | Global Intersection Cohomology of Quasimaps' Spaces | 21 pages, AmsLatex 1.1 | null | null | null | null | Let $C$ be a smooth projective curve of genus 0. Let $\CB$ be the variety of
complete flags in an $n$-dimensional vector space $V$. Given an $(n-1)$-tuple
$\alpha\in\BN[I]$ of positive integers one can consider the space $\CQ_\alpha$
of algebraic maps of degree $\alpha$ from $C$ to $\CB$. This space admits some
remar... | [
{
"version": "v1",
"created": "Fri, 14 Feb 1997 18:22:28 GMT"
}
] | 2016-08-30T00:00:00 | [
[
"Finkelberg",
"Michael",
"",
"Independent University of\n Moscow"
],
[
"Kuznetsov",
"Alexander",
"",
"Independent University of\n Moscow"
]
] | alg-geom | \section{Introduction}
\subsection{}
Let $C$ be a smooth projective curve of genus 0. Let $\CB$ be the variety
of complete flags in an $n$-dimensional vector space $V$.
Given an $(n-1)$-tuple $\alpha\in\BN[I]$
of positive integers one can consider the space $\CQ_\alpha$ of algebraic
maps of degree $\alpha$ from $C$ to... |
1997-02-28T16:42:10 | 9702 | alg-geom/9702016 | en | https://arxiv.org/abs/alg-geom/9702016 | [
"alg-geom",
"math.AG"
] | alg-geom/9702016 | Miles Reid | Miles Reid (Nagoya and Warwick) | McKay correspondence | V2 cured 2 misguided crossreferences and some errors of punctuation.
This v3 gives references sent in by listeners to this network, and centres
the graphics, a triumph of mind over computer manual! | null | null | Proc of Kinosaki conference (Nov 1996), and Warwick preprint 1997 | null | This is a rough write-up of my lecture at Kinosaki and two lectures at RIMS
workshops in Dec 1996, on work in progress that has not yet reached any really
worthwhile conclusion, but contains lots of fun calculations. History of Vafa's
formula, how the McKay correspondence for finite subgroups of SL(n,C) relates
to mi... | [
{
"version": "v1",
"created": "Tue, 25 Feb 1997 12:11:45 GMT"
},
{
"version": "v2",
"created": "Wed, 26 Feb 1997 09:02:58 GMT"
},
{
"version": "v3",
"created": "Fri, 28 Feb 1997 09:12:21 GMT"
}
] | 2016-08-30T00:00:00 | [
[
"Reid",
"Miles",
"",
"Nagoya and Warwick"
]
] | alg-geom | \section{Introduction}\label{sec:intro}
\begin{conjecture}[since 1992]\label{conj:1992}
$G\subset\SL(n,\C)$ is a finite subgroup. Assume that the quotient $X=\C^n/G$
has a crepant resolution $f\colon Y\to X$ (this just means that $K_Y=0$, so
that $Y$ is a ``noncompact Calabi--Yau manifold''). Then there exist
``natur... |
1997-02-03T09:31:26 | 9702 | alg-geom/9702003 | en | https://arxiv.org/abs/alg-geom/9702003 | [
"alg-geom",
"math.AG"
] | alg-geom/9702003 | Tohsuke Urabe | Tohsuke Urabe (Department of Mathematics Tokyo Metropolitan
University, Hachioji-shi, Tokyo, Japan) | Dual varieties and the duality of the second fundamental form | LaTeX2e+AmsLaTeX. 3 pages. This manuscript was submitted to
Proceedings of Symposium Real Analytic and Algebraic Singularities(IS(J held
at Nagoya University in September - October, 1996. Adobe PDF version is
available also at http://urabe-lab.math.metro-u.ac.jp/ | null | null | null | null | First, we consider a compact real-analytic irreducible subvariety $M$ in a
sphere and its dual variety $M^\vee$. We explain that two matrices of the
second fundamental forms for both varieties $M$ and $M^\vee$ can be regarded as
the inverse matrices of each other. Also generalization in hyperbolic space is
explained.... | [
{
"version": "v1",
"created": "Mon, 3 Feb 1997 08:32:45 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Urabe",
"Tohsuke",
"",
"Department of Mathematics Tokyo Metropolitan\n University, Hachioji-shi, Tokyo, Japan"
]
] | alg-geom | \section{Spherical case}
\label{sphere}
In this article I would like to explain main ideas
in my recent results
on duality of the second fundamental form.
(Urabe\cite{{urabe;dual}}.)
Theory of dual varieties in the complex algebraic geometry is
very interesting.
(Griffiths and Harris~\cite{griffiths-harris;geo},
K... |
1997-02-27T21:41:37 | 9702 | alg-geom/9702019 | en | https://arxiv.org/abs/alg-geom/9702019 | [
"alg-geom",
"math.AG"
] | alg-geom/9702019 | Alan Durfee | Alan H. Durfee | Five Definitions of Critical Point at Infinity | 20 pages, Latex, 4 figures | null | null | null | null | This survey paper discusses five equivalent ways of defining a ``critical
point at infinity'' for a complex polynomial of two variables.
| [
{
"version": "v1",
"created": "Thu, 27 Feb 1997 20:41:22 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Durfee",
"Alan H.",
""
]
] | alg-geom | \section{#1}}
\newcounter{mycounter}[section]
\renewcommand{\themycounter}{\arabic{section}.\arabic{mycounter}}
\newenvironment{theorem}%
{\medskip
\refstepcounter{mycounter}
{\bf \noindent Theorem \themycounter. \ } \begin{em} }%
{\end{em} \medskip }
\newenvironment{proposition}%
{\medskip
\refstepcou... |
1997-02-27T07:20:18 | 9702 | alg-geom/9702018 | en | https://arxiv.org/abs/alg-geom/9702018 | [
"alg-geom",
"math.AG"
] | alg-geom/9702018 | Furuya Masako | Masako Furuya | On $\delta_m$ constant locus of versal deformations of nondegenerate
hypersurface simple K3 singularities | AMS-LaTeX v1.2, 35 pages with 5 figures | null | null | null | null | Hypersurface simple K3 singularities defined by nondegenerate
quasi-homogeneous polynomials are classified into ninety five classes in term
of the weight of the polynomial by T. Yonemura. We consider versal deformations
of them. It has been conjectured that the stratum $\mu$ =const of the versal
deformation of any no... | [
{
"version": "v1",
"created": "Thu, 27 Feb 1997 06:18:48 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Furuya",
"Masako",
""
]
] | alg-geom | \section*{Introduction}
Simple $K3$ singularities are regarded as natural generalizations in
three-dimensional case of simple elliptic singularities. The notion of a
simple $K3$ singularity was defined by S. Ishii and K. Watanabe [IW] as a
three-dimensional Gorenstein purely elliptic singularity of (0,2)-type,
... |
1997-02-20T17:14:20 | 9702 | alg-geom/9702004 | en | https://arxiv.org/abs/alg-geom/9702004 | [
"alg-geom",
"math.AG"
] | alg-geom/9702004 | Alice Silverberg | A. Silverberg and Yu. G. Zarhin | Semistable reduction of abelian varieties over extensions of small
degree | LaTeX2e | null | null | null | null | We obtain necessary and sufficient conditions for abelian varieties to
acquire semistable reduction over fields of low degree. Our criteria are
expressed in terms of torsion points of small order defined over unramified
extensions.
| [
{
"version": "v1",
"created": "Mon, 3 Feb 1997 20:20:45 GMT"
},
{
"version": "v2",
"created": "Thu, 20 Feb 1997 16:14:15 GMT"
}
] | 2016-08-30T00:00:00 | [
[
"Silverberg",
"A.",
""
],
[
"Zarhin",
"Yu. G.",
""
]
] | alg-geom | \section{Introduction}
In this paper we obtain criteria for
abelian varieties to acquire semistable reduction over fields
of certain given (small) degrees. Our criteria are expressed
in terms of unramified torsion points.
Suppose that $X$ is an abelian variety defined over a field
$F$, and $n$ is a positive intege... |
1997-02-06T20:31:38 | 9702 | alg-geom/9702008 | en | https://arxiv.org/abs/alg-geom/9702008 | [
"alg-geom",
"math.AG"
] | alg-geom/9702008 | Eleny-Nicoleta Ionel | Eleny-Nicoleta Ionel, Thomas H. Parker | The Gromov Invariants of Ruan-Tian and Taubes | AMS-LaTeX, 11 pages | null | null | null | null | Taubes has recently defined Gromov invariants for symplectic four-manifolds
and related them to the Seiberg-Witten invariants. Independently, Ruan and Tian
defined symplectic invariants based on ideas of Witten. In this note, we show
that Taubes' Gromov invariants are equal to certain combinations of Ruan-Tian
invari... | [
{
"version": "v1",
"created": "Thu, 6 Feb 1997 19:31:31 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Ionel",
"Eleny-Nicoleta",
""
],
[
"Parker",
"Thomas H.",
""
]
] | alg-geom | \section{Gromov Invariants}
Fix a closed symplectic four-manifold $(X,\omega)$. Following the ideas of
Gromov and Donaldson, one can define
symplectic invariants by introducing an almost complex structure $J$ and
counting (with orientation) the number
of $J$-holomorphic curves on $X$ satisfying certain constrain... |
1993-12-14T14:07:14 | 9312 | alg-geom/9312007 | en | https://arxiv.org/abs/alg-geom/9312007 | [
"alg-geom",
"math.AG"
] | alg-geom/9312007 | null | Gerd Dethloff, Georg Schumacher, Pit-Mann Wong | Hyperbolicity of the complement of plane algebraic curves | LaTeX | Amer. J. Math. 117, 573-599 (1995) | null | null | null | The paper is a contribution of the conjecture of Kobayashi that the
complement of a generic plain curve of degree at least five is hyperbolic. The
main result is that the complement of a generic configuration of three quadrics
is hyperbolic and hyperbolically embedded as well as the complement of two
quadrics and a l... | [
{
"version": "v1",
"created": "Tue, 14 Dec 1993 13:04:27 GMT"
}
] | 2014-12-01T00:00:00 | [
[
"Dethloff",
"Gerd",
""
],
[
"Schumacher",
"Georg",
""
],
[
"Wong",
"Pit-Mann",
""
]
] | alg-geom | \section{Introduction}
Hyperbolic manifolds have been studied in complex analysis as the
generalizations of hyperbolic Riemann surfaces to higher dimensions.
Moreover, the theory of hyperbolic manifolds is closely related to other
areas (cf.\ eg. \cite{LA1}).
However, only very few quasi-projective (non closed) hyper... |
1996-02-27T06:25:20 | 9312 | alg-geom/9312011 | en | https://arxiv.org/abs/alg-geom/9312011 | [
"alg-geom",
"math.AG"
] | alg-geom/9312011 | Charles Walter | Charles H. Walter | Components of the Stack of Torsion-Free Sheaves of Rank 2 on Ruled
Surfaces | 16 pages, LATeX 2.09 | Math. Ann. 301 (1995), 699-715 | null | null | null | Let S be a ruled surface without sections of negative self-intersection. We
classify the irreducible components of the moduli stack of torsion-free sheaves
of rank 2 sheaves on S. We also classify the irreducible components of the
Brill-Noether loci in Hilb^N(P1xP1) given by W_N^0(D)={[X] | h^1(I_X(D)) >= 1 }
for D a... | [
{
"version": "v1",
"created": "Mon, 20 Dec 1993 15:03:46 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Walter",
"Charles H.",
""
]
] | alg-geom | \section{\@startsection{section}{1}{\z@}{-3.25ex plus
-1ex minus -.2ex}{1.5ex plus .2ex}{\large\bf}}
\def\subsection{\@startsection
{subsection}{2}{\z@}{3.25ex plus 1ex minus .2ex}{-0.5em}{\normalsize\sl}}
\def\subsubsection{\@startsection
{subsubsection}{3}{\z@}{3.25ex plus 1ex minus .2ex}{-0.5em}{\normalsize\sl}}
... |
1994-11-07T06:20:07 | 9312 | alg-geom/9312004 | en | https://arxiv.org/abs/alg-geom/9312004 | [
"alg-geom",
"math.AG"
] | alg-geom/9312004 | Alexander Polischuk | A. Polishchuk | On Koszul property of the homogeneous coordinate ring of a curve | 17 pages, Latex | null | null | null | null | The following corollary has been added: for general tetragonal curve $C$ of
genus $g\ge 9$ the homogeneous coordinate ring of $C$ defined by the line
bundle $K(-T)$, where $K$ is the canonical class, $T$ is the tetragonal series,
is Koszul. Also some misprints are corrected.
| [
{
"version": "v1",
"created": "Wed, 8 Dec 1993 23:25:56 GMT"
},
{
"version": "v2",
"created": "Fri, 4 Nov 1994 18:27:46 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Polishchuk",
"A.",
""
]
] | alg-geom | \section{Introduction}
This paper is devoted to Koszul property of the homogeneous
coordinate algebra of a smooth complex algebraic curve in the
projective space (the notion of a Koszul algebra
is some homological refinement of the notion of a quadratic algebra,
for precise definition see next section). It
grew out f... |
1993-12-20T15:58:43 | 9312 | alg-geom/9312010 | en | https://arxiv.org/abs/alg-geom/9312010 | [
"alg-geom",
"math.AG"
] | alg-geom/9312010 | Charles Walter | Charles H. Walter | On the Harder-Narasimhan Filtration for Coherent Sheaves on P2: I | 14 pages, LATeX 2.09 | null | null | null | null | Let E be a torsion-free sheaf on P2. We give an effective method which uses
the Hilbert function of E to construct a weak version of the Harder-Narasimhan
filtration of a torsion-free sheaf on P2 subject only to the condition that E
be sufficiently general among sheaves with that Hilbert function. This
algorithm uses... | [
{
"version": "v1",
"created": "Mon, 20 Dec 1993 15:00:43 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Walter",
"Charles H.",
""
]
] | alg-geom | \section{\@startsection{section}{1}{\z@}{-3.25ex plus
-1ex minus -.2ex}{1.5ex plus .2ex}{\large\bf}}
\def\subsection{\@startsection
{subsection}{2}{\z@}{3.25ex plus 1ex minus .2ex}{-0.5em}{\normalsize\sl}}
\def\subsubsection{\@startsection
{subsubsection}{3}{\z@}{3.25ex plus 1ex minus .2ex}{-0.5em}{\normalsize\sl}}
... |
1993-12-14T14:10:39 | 9312 | alg-geom/9312008 | en | https://arxiv.org/abs/alg-geom/9312008 | [
"alg-geom",
"math.AG"
] | alg-geom/9312008 | null | Gerd Dethloff, Georg Schumacher, Pit-Mann Wong | On the Hyperbolicity of the Complements of Curves in Algebraic Surfaces:
The Three Component Case | 26 pages, LaTeX | Duke Math. J. 78, 193-212 (1995) | null | null | null | The paper is a contribution to the conjecture of Kobayashi that the
complement of a generic curve in the projective plane is hyperbolic, provided
the degree is at least five. Previously the authors treated the cases of two
quadrics and a line and three quadrics. The main results are Let C be the union
of three curves... | [
{
"version": "v1",
"created": "Tue, 14 Dec 1993 13:06:20 GMT"
}
] | 2014-12-01T00:00:00 | [
[
"Dethloff",
"Gerd",
""
],
[
"Schumacher",
"Georg",
""
],
[
"Wong",
"Pit-Mann",
""
]
] | alg-geom | \section{Introduction} In complex analysis hyperbolic manifolds have
been studied extensively, with close relationships to other areas
(cf.\ eg. \cite{LA1}). Hyperbolic manifolds are generalizations of
hyperbolic Riemann surfaces to higher dimensions. Despite the fact
that the general theory of hyperbolic manifolds is ... |
1993-12-14T12:40:04 | 9312 | alg-geom/9312006 | en | https://arxiv.org/abs/alg-geom/9312006 | [
"alg-geom",
"math.AG"
] | alg-geom/9312006 | Fabrizio Broglia | F. Acquistapace, F.Broglia, M.Pilar Velez | An algorithmic criterion for basicness in dimension 2 | 23 pages, amslatex (+bezier.sty) report: 1.89.(766) october 1993 | null | null | null | null | We give a constructive procedure to check basicness of open (or closed)
semialgebraic sets in a compact, non singular, real algebraic surface $X$. It
is rather clear that if a semialgebraic set $S$ can be separated from each
connected component of $X\setminus(S\cup\frz S)$ (when $\frz S$ stands for the
Zariski closur... | [
{
"version": "v1",
"created": "Tue, 14 Dec 1993 10:58:46 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Acquistapace",
"F.",
""
],
[
"Broglia",
"F.",
""
],
[
"Velez",
"M. Pilar",
""
]
] | alg-geom | \section*{Introduction.}
In this paper we give a constructive procedure to
check basicness of open (or closed) semialgebraic sets in a compact,
non singular, real algebraic surface $X$. It is rather clear that if a
semialgebraic set $S$ can be separated
from each connected component of $X\setminus(S\cup\partial _{\rm ... |
1994-01-24T21:31:29 | 9312 | alg-geom/9312012 | en | https://arxiv.org/abs/alg-geom/9312012 | [
"alg-geom",
"math.AG"
] | alg-geom/9312012 | Israel Vainsencher | Israel Vainsencher | Enumeration of $n$-fold tangent hyperplanes to a surface | 34 pages, Latex (Corrects Latex errors of previous version, minor
changes) | null | null | null | null | For each $1\leq n\leq6$ we present formulas for the number of $n-$nodal
curves in an $n-$dimensional linear system on a smooth, projective surface.
This yields in particular the numbers of rational curves in the system of
hyperplane sections of a generic $K3-$surface imbedded in \p{n} by a complete
system of curves o... | [
{
"version": "v1",
"created": "Tue, 21 Dec 1993 21:29:13 GMT"
},
{
"version": "v2",
"created": "Mon, 24 Jan 1994 14:43:01 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Vainsencher",
"Israel",
""
]
] | alg-geom | \section{Introduction} \normalsize
The purpose of this article is to present formulas for the number of
$n-$nodal curves in an $n-$dimensional linear system on a smooth,
projective surface for $1\leq n\leq6$.
The method also yields formulas for the number of multi--tangent planes
to a hypersurface. In particular, it e... |
1996-06-03T11:04:21 | 9606 | alg-geom/9606001 | en | https://arxiv.org/abs/alg-geom/9606001 | [
"alg-geom",
"math.AC",
"math.AG"
] | alg-geom/9606001 | Peter Schenzel | Peter Schenzel | Descent from the form ring and Buchsbaum rings | To appear in Comm. Algebra Latex2e | null | null | null | null | There is a spectral sequence technique in order to estimate the local
cohomology of a ring by the local cohomology of a certain form ring. As
applications there are information on the descent of homological properties
(Cohen-Macaulay, Buchsbaum etc.) from the form ring to the ring itself. In the
case of Buchsbaum rin... | [
{
"version": "v1",
"created": "Mon, 3 Jun 1996 10:00:59 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Schenzel",
"Peter",
""
]
] | alg-geom | \section{Introduction and Main Results}
One of the major problems in commutative algebra is to recover
information about a commutative ring $A$ from known properties
of the form ring $G := G_A(\mathfrak q) = \oplus_{n\geq 0}
{\mathfrak q}^n/{\mathfrak q}^{n+1}$ with respect to some
ideal $\mathfrak q$ of $A$. Ther... |
1996-06-20T17:00:23 | 9606 | alg-geom/9606014 | en | https://arxiv.org/abs/alg-geom/9606014 | [
"alg-geom",
"math.AG"
] | alg-geom/9606014 | null | Sheldon Katz, Zhenbo Qin, and Yongbin Ruan | Composition law and Nodal genus-2 curves in P^2 | 13 pages, AMS-TeX | null | null | OSU Math 1996-18 | null | Recently, there has been great interest in the application of composition
laws to problems in enumerative geometry. Using the moduli space of stable
maps, we compute the number of irreducible, reduced, nodal, degree-$d$
genus-$2$ plane curves whose normalization has a fixed complex structure and
which pass through $3... | [
{
"version": "v1",
"created": "Thu, 20 Jun 1996 15:01:23 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Katz",
"Sheldon",
""
],
[
"Qin",
"Zhenbo",
""
],
[
"Ruan",
"Yongbin",
""
]
] | alg-geom | \section{1. Introduction}
Enumerative algebraic geometry is an old field of algebraic geometry.
There are many fascinating problems going back more than a hundred years
to the Italian school. The most famous one is perhaps
the counting problem for the number of holomorphic curves in $\Pee^2$.
There are in fact two... |
1996-09-28T13:10:14 | 9606 | alg-geom/9606010 | en | https://arxiv.org/abs/alg-geom/9606010 | [
"alg-geom",
"math.AG",
"math.QA",
"q-alg"
] | alg-geom/9606010 | Vladimir Hinich | Vladimir Hinich | Descent of Deligne groupoids | Minor corrections made AMSLaTeX v 1.2 (Compatibility mode) | null | null | null | null | To any non-negatively graded dg Lie algebra $g$ over a field $k$ of
characteristic zero we assign a functor $\Sigma_g: art/k \to Kan$ from the
category of commutative local artinian $k$-algebras with the residue field $k$
to the category of Kan simplicial sets. There is a natural homotopy equivalence
between $\Sigma_... | [
{
"version": "v1",
"created": "Tue, 11 Jun 1996 07:55:20 GMT"
},
{
"version": "v2",
"created": "Wed, 25 Sep 1996 17:22:16 GMT"
},
{
"version": "v3",
"created": "Sat, 28 Sep 1996 11:07:28 GMT"
}
] | 2016-08-30T00:00:00 | [
[
"Hinich",
"Vladimir",
""
]
] | alg-geom | \section{Introduction}
\subsection{}
\label{i1}
Let $\fg$ be a dg Lie algebra over a field $k$ of characteristic zero
concentrated in non-negative degrees. The algebra $\fg$ defines a functor
$$ \CC_{\fg}:\art/k\to\Grp$$
from the category of local artinian $k$-algebras with the residue field $k$
to the category of gro... |
2009-11-28T03:16:12 | 9606 | alg-geom/9606006 | en | https://arxiv.org/abs/alg-geom/9606006 | [
"alg-geom",
"math.AG"
] | alg-geom/9606006 | Dmitri O. Orlov | Dmitri Orlov | Equivalences of derived categories and K3 surfaces | 28 pages, LaTeX file | J. Math. Sci. (New York) 84 (1997), no. 5, 1361--1381 | null | null | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider derived categories of coherent sheaves on smooth projective
varieties. We prove that any equivalence between them can be represented by an
object on the product. Using this, we give a necessary and sufficient condition
for equivalence of derived categories of two K3 surfaces.
| [
{
"version": "v1",
"created": "Fri, 7 Jun 1996 12:29:42 GMT"
},
{
"version": "v2",
"created": "Tue, 11 Jun 1996 10:37:02 GMT"
},
{
"version": "v3",
"created": "Fri, 1 Nov 1996 12:54:27 GMT"
},
{
"version": "v4",
"created": "Wed, 17 Dec 1997 13:00:12 GMT"
},
{
"ver... | 2009-11-28T00:00:00 | [
[
"Orlov",
"Dmitri",
""
]
] | alg-geom | \section*{Introduction}
Let $\db{X}$ be the bounded derived category of coherent sheaves on a smooth
projective variety $X.$ The category $\db{X}$ has the structure of a triangulated
category (see \cite{Ver}, \cite{GM}). We shall consider $\db{X}$
as a triangulated category.
In this paper we are concerned with the pr... |
1996-06-06T13:40:26 | 9606 | alg-geom/9606003 | en | https://arxiv.org/abs/alg-geom/9606003 | [
"alg-geom",
"math.AG"
] | alg-geom/9606003 | V. Batyrev | Victor V. Batyrev, Yuri Tschinkel | Height Zeta Functions of Toric Varieties | 27 pages, AMS-LaTeX | null | null | LMENS-96-9 | null | We investigate analytic properties of height zeta functions of toric
varieties. Using the height zeta functions, we prove an asymptotic formula for
the number of rational points of bounded height with respect to an arbitrary
line bundle whose first Chern class is contained in the interior of the cone of
effective div... | [
{
"version": "v1",
"created": "Thu, 6 Jun 1996 11:36:04 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Batyrev",
"Victor V.",
""
],
[
"Tschinkel",
"Yuri",
""
]
] | alg-geom | \section{Introduction}
\bigskip
Let $X$ be a $d$-dimensional
algebraic variety defined over a number field $F$.
Denote by ${\cal L}=(L,\{\|\cdot\|_v\})$ a metrized line bundle on $X$ ,
i.e. a line bundle $L$ together with a family of $v$-adic metrics,
where $v$ runs over the set ${\operatorname{Val} }(F)$ of all va... |
1997-04-23T16:41:51 | 9606 | alg-geom/9606019 | en | https://arxiv.org/abs/alg-geom/9606019 | [
"alg-geom",
"dg-ga",
"hep-th",
"math.AG",
"math.DG"
] | alg-geom/9606019 | Misha Verbitsky | Dmitry Kaledin, Misha Verbitsky | Non-Hermitian Yang-Mills connections | 48 pages, LaTeX 2e | Selecta Math. 4 (1998) 279-320 | null | null | null | We study Yang-Mills connections on holomorphic bundles over complex K\"ahler
manifolds of arbitrary dimension, in the spirit of Hitchin's and Simpson's
study of flat connections. The space of non-Hermitian Yang-Mills (NHYM)
connections has dimension twice the space of Hermitian Yang-Mills connections,
and is locally ... | [
{
"version": "v1",
"created": "Mon, 1 Jul 1996 00:01:13 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Kaledin",
"Dmitry",
""
],
[
"Verbitsky",
"Misha",
""
]
] | alg-geom | \section{Introduction.}
\subsection{An overview}
In this paper we study non-Hermitian Yang-Mills (NHYM) connections
on a complex vector bundle ${\cal B}$ over a K\"ahler manifold.
By definition, a connection
$\nabla$ in ${\cal B}$ is Yang-Mills if its curvature $\Theta$
satisfies
\begin{equation} \label{intro-Yan... |
1996-06-27T15:32:07 | 9606 | alg-geom/9606017 | fr | https://arxiv.org/abs/alg-geom/9606017 | [
"alg-geom",
"math.AG"
] | alg-geom/9606017 | Emmanuel Ullmo | Emmanuel Ullmo | Positivite et discretion des points algebriques des courbes | null | null | null | null | null | We prove the discreteness of algebraic points (with respect to the Neron-Tate
height) on a curve of genus greater than one embedded in his jacobian. This
result was conjectured by Bogomolov. We also prove the positivity of the self
intersection of the admissible dualizing sheaf.
| [
{
"version": "v1",
"created": "Thu, 27 Jun 1996 13:32:11 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Ullmo",
"Emmanuel",
""
]
] | alg-geom | \section{Introduction}
Soient $K$ un corps de nombres et $\overline{K}$ sa cl\^oture alg\'ebrique. Soient $X_K$
une courbe propre, lisse, g\'eom\'etriquement connexe de genre $g\ge 2$ sur $K$ et
$J$ sa jacobienne. Soit $D_0$ un diviseur de
degr\'e 1 sur $X$ et $\phi_{D_0}$ le plongement de $X_K$ dans $J$
d\'efini p... |
1996-11-15T12:20:43 | 9606 | alg-geom/9606009 | en | https://arxiv.org/abs/alg-geom/9606009 | [
"alg-geom",
"math.AG"
] | alg-geom/9606009 | Francisco Jose Plaza Martin | A. \'Alvarez V\'azquez, J. M. Mu\~noz Porras, F. J. Plaza Mart\'in | The algebraic formalism of soliton equations over arbitrary base fields | Minor changes in Section 5 and References | Variedades Abelianas y Funciones Theta, Ap. Mat. Serie
Investigaci\'on No. 13, Sociedad Matem\'atica Mexicana, M\'exico 1998 | null | null | null | The aim of this paper is to offer an algebraic construction of
infinite-dimensional Grassmannians and determinant bundles (and therefore valid
for arbitrary base fields). As an application we construct the $\tau$-function
and formal Baker-Akhiezer functions over arbitrary fields, by proving the
existence of a ``forma... | [
{
"version": "v1",
"created": "Mon, 10 Jun 1996 18:09:23 GMT"
},
{
"version": "v2",
"created": "Fri, 15 Nov 1996 10:19:15 GMT"
}
] | 2016-08-15T00:00:00 | [
[
"Vázquez",
"A. Álvarez",
""
],
[
"Porras",
"J. M. Muñoz",
""
],
[
"Martín",
"F. J. Plaza",
""
]
] | alg-geom | \section{Introduction}
The aim of this paper is to offer an algebraic construction of
infinite-dimensional Grassmannians and determinant bundles. As an
application we construct the $\tau$-function and formal
Baker-Akhiezer functions over arbitrary fields, by proving the
existence of a ``formal geometry'' of local cur... |
1996-06-07T13:25:43 | 9606 | alg-geom/9606007 | en | https://arxiv.org/abs/alg-geom/9606007 | [
"alg-geom",
"math.AG"
] | alg-geom/9606007 | Joost van Hamel | Fr\'ed\'eric Mangolte and Joost van Hamel | Algebraic cycles and topology of real Enriques surfaces | 18 pages AMS-LaTeX v 1.2 | null | null | null | null | For a real Enriques surface Y we prove that every homology class in H_1(Y(R),
Z/2) can be represented by a real algebraic curve if and only if all connected
components of Y(R) are orientable. Furthermore, we give a characterization of
real Enriques surfaces which are Galois-Maximal and/or Z-Galois-Maximal and we
dete... | [
{
"version": "v1",
"created": "Fri, 7 Jun 1996 11:20:04 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Mangolte",
"Frédéric",
""
],
[
"van Hamel",
"Joost",
""
]
] | alg-geom | \subsubsection*{Acknowledgements}}{\par}
\begin{document}
\title[Real Enriques surfaces]{Algebraic cycles and topology \\
of real Enriques surfaces}
\author{Fr\'ed\'eric Mangolte\and Joost van Hamel}
\keywords{Algebraic cycles, Real algebraic surfaces, Enriques
surfaces, Galois-Maximality}
\subjclass{14C25 14P25... |
1996-06-10T14:01:56 | 9606 | alg-geom/9606008 | en | https://arxiv.org/abs/alg-geom/9606008 | [
"alg-geom",
"math.AG"
] | alg-geom/9606008 | Michal Kwiecinski | Michal Kwiecinski and Piotr Tworzewski | Finite sets in fibres of holomorphic maps | LaTeX v. 2.09, 16 pages | null | null | IMUJ preprint 1996/08, Jagiellonian Univ., Krakow | null | We consider the maximal number of arbitrary points in a special fibre that
can be simultaneously approached by points in one sequence of general fibres.
Several results about this topological invariant and their applications
describe the structure of holomorphic maps. In particular, we get a lower bound
on the number... | [
{
"version": "v1",
"created": "Mon, 10 Jun 1996 12:03:01 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Kwiecinski",
"Michal",
""
],
[
"Tworzewski",
"Piotr",
""
]
] | alg-geom | \section{Introduction.}
From the work of Thom \cite{Thom}, Fukuda \cite{Fukuda}
and Nakai \cite{Nakai}, it follows that one cannot stratify
arbitrary complex algebraic maps so as to have local topological
triviality, such as in the case of Whitney stratified spaces.
Indeed, an arbitrary complex map can have a locally... |
1997-04-01T15:34:01 | 9606 | alg-geom/9606015 | en | https://arxiv.org/abs/alg-geom/9606015 | [
"alg-geom",
"math.AG"
] | alg-geom/9606015 | Ines Quandt | Ines Quandt | On a relative version of the Krichever correspondence | 59 pages LaTeX with inputs of AMSTeX; In addition to some corrections
the main change consists in the extension of the Krichever correspondence to
all locally noetherian base schemes | Bayreuther Mathematische Schriften 52 (1997), p.1-74 | null | null | null | For a given base scheme, a correspondence is established between a class of
sheaves on curves over this base scheme and certain points of infinite
Grassmannians. This equivalence extends to a characterization of commutative
algebras of ordinary differential operators with coefficients in the ring of
formal power seri... | [
{
"version": "v1",
"created": "Fri, 21 Jun 1996 07:29:24 GMT"
},
{
"version": "v2",
"created": "Tue, 1 Apr 1997 13:36:31 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Quandt",
"Ines",
""
]
] | alg-geom | \section*{Preface}
This PhD thesis is the result of my work in the Graduiertenkolleg
"Geometrie und Nichtlineare Analysis" at
Humboldt University Berlin and in the DFG project KU 770/1-3.
\vspace{0.5cm}\\
It is published in the {\em Bayreuther Mathematische Schriften} {\bf 52}
(1997), p.1-74.
\vspace{0.5cm}\\
At ... |
1996-06-06T09:45:23 | 9606 | alg-geom/9606002 | en | https://arxiv.org/abs/alg-geom/9606002 | [
"alg-geom",
"math.AG"
] | alg-geom/9606002 | Rita Pardini | Rita Pardini | On the period map for abelian covers of algebraic varieties | LaTeX, 17 pages | null | null | null | null | We show that infinitesimal Torelli for $n$-forms holds for abelian covers of
algebraic varieties of dimension $n\ge 2$, under some explicit ampleness
assumptions on the building data of the cover. Moreover, we prove a variational
Torelli result for some families of abelian covers.
| [
{
"version": "v1",
"created": "Thu, 6 Jun 1996 08:38:16 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Pardini",
"Rita",
""
]
] | alg-geom | \section{Introduction}
\setcounter{defn}{0}
\setcounter{equation}{0}
This paper is devoted to the study of the period map for abelian covers
of smooth projective varieties of dimension $n\ge 2$. Our viewpoint is
very close to that of Green in \cite{suffampio}, namely we look for
results that hold for abelian covers... |
1995-10-12T06:39:56 | 9507 | alg-geom/9507010 | en | https://arxiv.org/abs/alg-geom/9507010 | [
"alg-geom",
"math.AG"
] | alg-geom/9507010 | Leonid Positselski | Leonid Positselski and Alexander Vishik | Koszul duality and Galois cohomology | AMS-LaTeX v.1.1, 10 pages, no figures. Replaced for tex code
correction (%&amslplain added) by request of www-admin | Math. Research Letters 2 (1995), no.6, p.771-781 | 10.4310/MRL.1995.v2.n6.a8 | null | null | It it shown that the Bloch-Kato conjecture on the norm residue homomorphism
$K^M(F)/l \to H^*(G_F,Z/l)$ follows from its (partially known) low-degree part
under the assumption that the Milnor K-theory algebra $K^M(F)/l$ modulo $l$ is
Koszul. This conclusion is a case of a general result on the cohomology of
nilpotent... | [
{
"version": "v1",
"created": "Tue, 11 Jul 1995 23:07:32 GMT"
},
{
"version": "v2",
"created": "Thu, 31 Aug 1995 02:00:06 GMT"
}
] | 2013-10-29T00:00:00 | [
[
"Positselski",
"Leonid",
""
],
[
"Vishik",
"Alexander",
""
]
] | alg-geom | \section{#1}\medskip}
\newcommand{\operatorname{coker}}{\operatorname{coker}}
\newcommand{\operatorname{id}}{\operatorname{id}}
\newcommand{\operatorname{char}}{\operatorname{char}}
\newcommand{\operatorname{Hom}}{\operatorname{Hom}}
\newcommand{\operatorname{Tor}}{\operatorname{Tor}}
\newcommand{\operatorname{Ext}}{\... |
1995-07-26T06:20:13 | 9507 | alg-geom/9507014 | en | https://arxiv.org/abs/alg-geom/9507014 | [
"alg-geom",
"math.AG"
] | alg-geom/9507014 | Leonid Positselski | Leonid Positselski | All strictly exceptional collections in $D^b_{coh}(P^m)$ consist of
vector bundles | LaTeX 2e, 6 pages, no figures; replaced to correct formatting
(amslatex to latex2e transition) and several misprints, no other changes | null | null | null | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | It is proved that any strictly exceptional collection generating the derived
category of coherent sheaves on a smooth projective variety X with \rk K_0(X) =
\dim X + 1 constists of locally free sheaves up to a common shift.
| [
{
"version": "v1",
"created": "Wed, 26 Jul 1995 01:38:39 GMT"
},
{
"version": "v2",
"created": "Sat, 26 Oct 2013 18:12:41 GMT"
}
] | 2013-10-29T00:00:00 | [
[
"Positselski",
"Leonid",
""
]
] | alg-geom | \section{Introduction}
Let $\k$ be a field and ${\cal D}$ be a $\k$-linear triangulated
category; we will denote, as usually, $\operatorname{Hom}^i(X,Y)=\operatorname{Hom}(X,Y[i])$
and $\operatorname{Hom^{\scriptscriptstyle\bullet}}(X,Y)=\bigoplus_i\operatorname{Hom}^i(X,Y)$.
An object $E\in{\cal O}b\>{\cal D}$ is c... |
1996-03-08T06:56:05 | 9507 | alg-geom/9507002 | en | https://arxiv.org/abs/alg-geom/9507002 | [
"alg-geom",
"math.AG"
] | alg-geom/9507002 | Christoph Sorger | Yves Laszlo and Christoph Sorger | The line bundles on the stack of parabolic $G$-bundles over curves and
their sections | LaTeX2e with package amsart, 31 pages, no figures. This is a revised
version of our paper (mainly, the introduction and the section on pfaffians
have been changed). The TeX file, as well as the .dvi and .ps files are also
available at ftp://ftp.mathp7.jussieu.fr/pub/sorger | null | null | null | null | Let $X$ be a smooth, complete and connected curve and $G$ be a simple and
simply connected algebraic group over $\comp$. We calculate the Picard group of
the moduli stack of quasi-parabolic $G$-bundles and identify the spaces of
sections of its members to the conformal blocs of Tsuchiya, Ueno and Yamada. We
describe ... | [
{
"version": "v1",
"created": "Wed, 5 Jul 1995 08:33:53 GMT"
},
{
"version": "v2",
"created": "Tue, 10 Oct 1995 12:39:17 GMT"
},
{
"version": "v3",
"created": "Tue, 5 Mar 1996 23:25:37 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Laszlo",
"Yves",
""
],
[
"Sorger",
"Christoph",
""
]
] | alg-geom | \section{Introduction.}
\subsection{}\label{th:Pic} Fix a simple and simply connected algebraic group
$G$ over $k=\comp$ and a Borel subgroup $B\subset G$. Let $X$ be a smooth,
complete and connected curve over $k$ and
$p_{1},\dots,p_{n}$ be distinct points of $X$, labeled by standard (\ie
containing
$B$) parabolic su... |
1995-08-09T06:20:26 | 9507 | alg-geom/9507017 | en | https://arxiv.org/abs/alg-geom/9507017 | [
"alg-geom",
"math.AG"
] | alg-geom/9507017 | Ron Donagi | Ron Donagi and Eyal Markman | Spectral curves, algebraically completely integrable Hamiltonian
systems, and moduli of bundles | Latex, We restore the page numbers which were inadvertently omitted.
The content stayed the same | null | null | null | null | This is the expanded text of a series of CIME lectures. We present an
algebro-geometric approach to integrable systems, starting with those which can
be described in terms of spectral curves. The prototype is Hitchin's system on
the cotangent bundle of the moduli space of stable bundles on a curve. A
variant involvin... | [
{
"version": "v1",
"created": "Mon, 31 Jul 1995 23:00:47 GMT"
},
{
"version": "v2",
"created": "Tue, 8 Aug 1995 15:35:29 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Donagi",
"Ron",
""
],
[
"Markman",
"Eyal",
""
]
] | alg-geom | \section{Introduction} \label{ch1}
The purpose of these notes is to present an
algebro-geometric point of view on several interrelated topics,
all involving integrable systems in symplectic-algebro-geometric
settings. These systems range from some very old examples, such
as the geodesic flow on an ellipsoid, th... |
1995-07-31T06:20:14 | 9507 | alg-geom/9507015 | en | https://arxiv.org/abs/alg-geom/9507015 | [
"alg-geom",
"math.AG"
] | alg-geom/9507015 | Brendan Hassett | Brendan Hassett | Correlation for Surfaces of General Type | AMSLaTeX. This version contains some minor corrections, and additions
to the references | null | null | null | null | The main geometric result of this paper is that given any family of surfaces
of general type f:X-->B, for sufficiently large n the fiber product X^n_B
dominates a variety of general type. This result is especially interesting when
it is combined with Lang's Conjecture. This states that for a variety V of
general type... | [
{
"version": "v1",
"created": "Wed, 26 Jul 1995 23:27:19 GMT"
},
{
"version": "v2",
"created": "Sun, 30 Jul 1995 16:50:12 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Hassett",
"Brendan",
""
]
] | alg-geom | \section{Introduction}
The purpose of this paper is to prove the following theorem:
\begin{thm}[Correlation Theorem for Surfaces]
Let $f:X \longrightarrow B$ be a proper morphism of integral
varieties, whose general fiber is an integral surface of general
type. Then for $n$ sufficiently large, $X^n_B$ admits a dominan... |
1995-07-20T06:20:10 | 9507 | alg-geom/9507011 | en | https://arxiv.org/abs/alg-geom/9507011 | [
"alg-geom",
"math.AG"
] | alg-geom/9507011 | Stephan Endrass | Stephan Endrass | A Projective Surface of Degree Eight with 168 Nodes | LaTeX 2.09 with amssymbols | null | null | null | null | The estimate for the maximal number of ordinary double points of a projective
surface of degree eight is improved to $168\leq\mu(8)\leq 174$ by constructing
a projective surface of degree eight with 168 nodes.
| [
{
"version": "v1",
"created": "Wed, 19 Jul 1995 14:08:27 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Endrass",
"Stephan",
""
]
] | alg-geom | \section*{Introduction}
Consider algebraic surfaces in complex projective
threespace ${\Bbb P}_3$, denote by a {\em node} of such
a surface an ordinary double point and by $\mu\left(d\right)$ the maximal number of
nodes of an algebraic surface of degree $d$ in ${\Bbb P}_3$
with no further degeneracies.
This note shows ... |
1995-10-02T05:20:11 | 9507 | alg-geom/9507012 | en | https://arxiv.org/abs/alg-geom/9507012 | [
"alg-geom",
"math.AG"
] | alg-geom/9507012 | Nakajima Hiraku | Hiraku Nakajima | Heisenberg algebra and Hilbert schemes of points on projective surfaces | AMS-LaTeX v. 1.1, 16 pages | null | null | null | null | I have just replaced the first line by %&amslplain in order to be compiled by
AMS-LaTeX.
| [
{
"version": "v1",
"created": "Thu, 20 Jul 1995 05:04:25 GMT"
},
{
"version": "v2",
"created": "Fri, 29 Sep 1995 23:03:44 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Nakajima",
"Hiraku",
""
]
] | alg-geom | \section{Introduction}
The purpose of this paper is to throw a bridge between two seemingly
unrelated subjects. One is the Hilbert scheme of points on projective
surfaces, which has been intensively studied by various people (see
e.g., \cite{Iar,ES,Got,Go-book}). The other is the infinite
dimensional Heisenberg algebra... |
1995-07-10T06:20:21 | 9507 | alg-geom/9507004 | en | https://arxiv.org/abs/alg-geom/9507004 | [
"alg-geom",
"math.AG"
] | alg-geom/9507004 | Mikhail Zaidenberg | H. Flenner and M. Zaidenberg | On a class of rational cuspidal plane curves | LaTeX 30 pages, author-supplied DVI file available at
http://www.math.duke.edu/preprints/95-00.dvi | null | null | Duke preprint DUKE-M-95-00 | null | We obtain new examples and the complete list of the rational cuspidal plane
curves $C$ with at least three cusps, one of which has multiplicity ${\rm
deg}\,C - 2$. It occurs that these curves are projectively rigid. We also
discuss the general problem of projective rigidity of rational cuspidal plane
curves.
| [
{
"version": "v1",
"created": "Fri, 7 Jul 1995 13:12:49 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Flenner",
"H.",
""
],
[
"Zaidenberg",
"M.",
""
]
] | alg-geom | \section{On multiplicity sequences}
\noindent {\bf 1.1. Definition.} Let $(C, \,P) \subset ({\bf C}^2,\,P)$ be an irreducible
analytic plane curve germ, and let $${\bf C}^2 = V_0 \qquad
{\stackrel{\sigma_1}{\longleftarrow}} \qquad V_1 \qquad
{\stackrel{\sigma_2}{\longleftarrow}} \qquad \cdots \qquad
{\stackrel{\sigma_... |
1995-07-10T06:20:26 | 9507 | alg-geom/9507006 | en | https://arxiv.org/abs/alg-geom/9507006 | [
"alg-geom",
"math.AG"
] | alg-geom/9507006 | Jeroen Spandaw | Jeroen G. Spandaw | A Noether-Lefschetz theorem for vector bundles | 5 pages, no figures; LaTeX2e, should also work with LaTeX 2.09 with
NFSS | null | null | null | null | In this note we use the monodromy argument to prove a Noether-Lefschetz
theorem for vector bundles.
| [
{
"version": "v1",
"created": "Fri, 7 Jul 1995 14:36:41 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Spandaw",
"Jeroen G.",
""
]
] | alg-geom | \section{Introduction}\pagenumbering{arabic}
Let $X$ be a smooth complex projective manifold of dimension $n$ and let $E$
be a very ample vector bundle on $X$ of rank $r$. This means that the
tautological quotient line bundle $L$ on the bundle
$Y={\Bbb P}(E^\ast)$ of hyperplanes in $E$ is very ample.
For almost all $s... |
1995-07-05T06:20:14 | 9507 | alg-geom/9507001 | en | https://arxiv.org/abs/alg-geom/9507001 | [
"alg-geom",
"math.AG"
] | alg-geom/9507001 | Iwamoto Masayuki | Masayuki Iwamoto | General n-canonical divisors on two-dimensional smoothable
semi-log-terminal singularities | AMSLaTeX v 1.1 | null | null | null | null | In this paper we calculate genaral n-canonical divisors on smoothable
semi-log-terminal singularities in dimension 2, in other words, the full
sheaves associated to the double dual of the nth tensor power of the dualizing
sheaves of these singularities. And as its application we give the inequality
which bound the Go... | [
{
"version": "v1",
"created": "Tue, 4 Jul 1995 07:46:34 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Iwamoto",
"Masayuki",
""
]
] | alg-geom | \section{Introduction}
This paper is devoted to some fundumental calculation on
2-dimensional smoothable semi-log-terminal singularities.
If we study minimal or canonical models of one parameter degeneration
of algebraic surfaces, we must treat singularities that appear in
the central fiber.
Smoothable semi-log-termin... |
1995-07-10T06:20:23 | 9507 | alg-geom/9507005 | en | https://arxiv.org/abs/alg-geom/9507005 | [
"alg-geom",
"math.AG"
] | alg-geom/9507005 | Mikhail Zaidenberg | S. Orevkov and M. Zaidenberg | On the number of singular points of plane curves | LaTeX, 24 pages with 3 figures, author-supplied DVI file available at
http://www.math.duke.edu/preprints/95-00.dvi | null | null | Duke preprint DUKE-M-95-00 | null | This is an extended, renovated and updated report on a joint work which the
second named author presented at the Conference on Algebraic Geometry held at
Saitama University, 15-17 of March, 1995. The main result is an inequality for
the numerical type of singularities of a plane curve, which involves the degree
of th... | [
{
"version": "v1",
"created": "Fri, 7 Jul 1995 13:21:11 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Orevkov",
"S.",
""
],
[
"Zaidenberg",
"M.",
""
]
] | alg-geom | \section{Asymptotics of the number
of ordinary cusps}
We start with a brief survey of known results in the simplest case of ordinary
cusps.
It is well known that for a nodal plane curve $D \subset {\bf P}^2$ of degree $d$
the number of nodes can be an arbitrary non--negative integer allowed by the
genus formula, i... |
1997-06-02T18:22:22 | 9612 | alg-geom/9612004 | en | https://arxiv.org/abs/alg-geom/9612004 | [
"alg-geom",
"hep-th",
"math.AG"
] | alg-geom/9612004 | Ezra Getzler | Ezra Getzler (Northwestern University) | Intersection theory on $\Mbar_{1,4}$ and elliptic Gromov-Witten
invariants | 25 pages. amslatex-1.2. This is the revised version which will appear
in J. Amer. Math. Soc | null | null | MPI 96-161 | null | The WDVV equation is satisfied by the genus 0 correlation functions of any
topological field theory in two dimensions coupled to topological gravity, and
may be used to determine the genus 0 (rational) Gromov-Witten invariants of
many projective varieties (as was done for projective spaces by Kontsevich).
In this p... | [
{
"version": "v1",
"created": "Fri, 6 Dec 1996 15:07:57 GMT"
},
{
"version": "v2",
"created": "Mon, 2 Jun 1997 16:24:27 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Getzler",
"Ezra",
"",
"Northwestern University"
]
] | alg-geom | \section{Intersection theory on $\overline{\mathcal{M}}_{1,4}$}
In this section, we calculate the relations among certain codimension two
cycles in $\overline{\mathcal{M}}_{1,4}$; one such relation was known, and we find that
there is one new one.
First, we assign names to the codimension $1$ strata of
$\overline{\ma... |
1996-12-18T03:27:05 | 9612 | alg-geom/9612013 | en | https://arxiv.org/abs/alg-geom/9612013 | [
"alg-geom",
"math.AG"
] | alg-geom/9612013 | Misha S. Verbitsky | Misha Verbitsky | Desingularization of singular hyperkaehler varieties II | LaTeX 2e, 15 pages. This paper can be read independently from the
first part. `Desingularization part I' appeared in alg-geom/9611015 | null | null | null | null | This is a second part of alg-geom/9611015. We construct a natural
hyperkaehler desingularization for all singular hyperkaehler varieties. The
desingularization theorem was proven in alg-geom/9611015 under additional
assumption of local homogeneity. Here we show that local homogeneity is
redundant: every singular hype... | [
{
"version": "v1",
"created": "Wed, 18 Dec 1996 02:26:57 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Verbitsky",
"Misha",
""
]
] | alg-geom | \section{Introduction}
A hyperk\"ahler manifold is a Riemannian manifold with an action
of a quaternion algebra $\Bbb H$ in its tangent bundle, such that
for all $I\in \Bbb H$, $I^2=-1$, $I$ establishes a complex,
K\"ahler structure on $M$
(see \ref{_hyperkahler_manifold_Definition_} for details).
We extend this defi... |
1996-12-07T21:10:17 | 9612 | alg-geom/9612007 | en | https://arxiv.org/abs/alg-geom/9612007 | [
"alg-geom",
"math.AG"
] | alg-geom/9612007 | Donu Arapura | Donu Arapura and Pramathanath Sastry | Intermediate Jacobians of moduli spaces | AMS-LaTeX, 16 pages | null | null | null | null | Let $SU_X(n,L)$ be the moduli space of rank n semistable vector bundles with
fixed determinant L on a smooth projective genus g curve X. Let $SU_X^s(n,L)$
denote the open subset parametrizing stable bundles. We show that if g>3 and n
> 1, then the mixed Hodge structure on $H^3(SU_X^s(n, L))$ is pure of type
${(1,2),(... | [
{
"version": "v1",
"created": "Sat, 7 Dec 1996 20:09:24 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Arapura",
"Donu",
""
],
[
"Sastry",
"Pramathanath",
""
]
] | alg-geom | \section{Introduction}\label{s:intro}
We work throughout over the complex numbers ${\Bbb C}$, i.e. all schemes are over
${\Bbb C}$ and all maps of schemes are maps of ${\Bbb C}$-schemes. A curve, unless
otherwise stated, is a smooth complete curve. Points mean geometric points.
We will, as is usual in such situations, ... |
1996-12-11T08:32:54 | 9612 | alg-geom/9612008 | en | https://arxiv.org/abs/alg-geom/9612008 | [
"alg-geom",
"math.AG"
] | alg-geom/9612008 | Jim Bryan | Jim Bryan and Marc Sanders | Instantons on $S^{4}$ and $\cpbar $, rank stabilization, and Bott
periodicity | 20 pages, keywords: instantons, holomorphic bundles, Bott periodicity
LaTeX2e | null | null | null | null | We study the large rank limit of the moduli spaces of framed bundles on the
projective plane and the blown-up projective plane. These moduli spaces are
identified with various instanton moduli spaces on the 4-sphere and $\cpbar $,
the projective plane with the reverse orientation. We show that in the direct
limit top... | [
{
"version": "v1",
"created": "Wed, 11 Dec 1996 07:35:54 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Bryan",
"Jim",
""
],
[
"Sanders",
"Marc",
""
]
] | alg-geom | \section{Introduction}
Let $\M{k}{G_{n}}(X)$ denote the space of (based) $G_{n}$-instantons on $X$
where $G_{n}$ is $SU(n)$, $SO(n)$, or $Sp(n/2)$. In 1989, Taubes
\cite{Tau-stable} showed that there is a ``gluing'' map
$\M{k}{G_{n}}(X)\hookrightarrow \M{k'}{G_{n}}(X)$ when $k'>k$.
He proved that in the direct limit t... |
1996-12-13T20:19:36 | 9612 | alg-geom/9612012 | en | https://arxiv.org/abs/alg-geom/9612012 | [
"alg-geom",
"hep-th",
"math.AG"
] | alg-geom/9612012 | Rolf Schimmrigk | Rolf Schimmrigk | Scaling Behavior on the Space of Calabi-Yau Manifolds | 11 pages, 4 eps figs Latex | null | null | BONN-TH-96-13 | null | Recent work is reviewed which suggests that certain universal quantities,
defined for all Calabi-Yau manifolds, exhibit a specific behavior which is not
present for general K\"ahler manifolds. The variables in question, natural from
a mathematical perspective, are of physical importance because they determine
aspects... | [
{
"version": "v1",
"created": "Thu, 12 Dec 1996 16:46:01 GMT"
},
{
"version": "v2",
"created": "Fri, 13 Dec 1996 19:18:59 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Schimmrigk",
"Rolf",
""
]
] | alg-geom | \section*{Acknowledgment}
It is a pleasure to thank Philip Candelas, Dimitrios Dais,
Xenia de la Ossa, Ed Derrick, Michael Flohr, Ariane Frey,
Jerry Hinnefeld, Vadim Kaplunovsky, Jack Morse, Werner Nahm, Steve Shore,
and especially Andreas Honecker, Monika Lynker and Katrin Wendland
for discussions.
I'm grateful to the... |
1997-04-23T16:37:10 | 9612 | alg-geom/9612016 | en | https://arxiv.org/abs/alg-geom/9612016 | [
"alg-geom",
"math.AG"
] | alg-geom/9612016 | Dmitry Kaledin | D. Kaledin | Integrability of the twistor space for a hypercomplex manifold | 9 pages, Latex2e | null | null | null | null | A hypercomplex manifold is by definition a smooth manifold equipped with two
anticommuting integrable almost complex structures. For example, every
hyperkaehler manifold is canonically hypercomplex (the converse is not true).
For every hypercomplex manifold M, the two almost complex structures define a
smooth action ... | [
{
"version": "v1",
"created": "Wed, 18 Dec 1996 20:14:58 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Kaledin",
"D.",
""
]
] | alg-geom | \section*{Introduction}
A {\em hyperk\"ahler manifold} is by definition a Riemannian
manifold eqipped with a smooth parallel action of the algebra of
quaternions on its tangent bundle. Hyperk\"ahler manifolds were
introduced by Calabi in \cite{C} and have since been the subject of
much research. They have been shown ... |
1998-01-19T10:34:51 | 9612 | alg-geom/9612011 | en | https://arxiv.org/abs/alg-geom/9612011 | [
"alg-geom",
"math.AG"
] | alg-geom/9612011 | null | Atsushi Moriwaki | Relative Bogomolov's inequality and the cone of positive divisors on the
moduli space of stable curves | Version 4.5 (33 pages). This paper will appear in Journal of AMS | null | null | null | null | Let f : X --> Y be a projective morphism of smooth algebraic varieties over
an algebraically closed field of characteristic zero with dim f = 1. Let E be a
vector bundle of rank r on X. In this paper, we would like to show that if X_y
is smooth and E_y is semistable for some point y of Y, then f_* (2r c_2(E) -
(r-1) ... | [
{
"version": "v1",
"created": "Thu, 12 Dec 1996 14:48:28 GMT"
},
{
"version": "v2",
"created": "Fri, 3 Jan 1997 14:01:48 GMT"
},
{
"version": "v3",
"created": "Thu, 30 Jan 1997 15:18:32 GMT"
},
{
"version": "v4",
"created": "Mon, 7 Apr 1997 06:07:32 GMT"
},
{
"ver... | 2008-02-03T00:00:00 | [
[
"Moriwaki",
"Atsushi",
""
]
] | alg-geom | \section*{Introduction}
\renewcommand{\theTheorem}{\Alph{Theorem}}
Throughout this paper, we fix an algebraically closed field $k$.
Let $f : X \to Y$ be a surjective and
projective morphism of quasi-projective varieties over $k$ with $\dim f = 1$.
Let $E$ be a vector bundle of rank $r$ on $X$. Then, we define
the {\em... |
1998-03-12T14:07:15 | 9612 | alg-geom/9612010 | en | https://arxiv.org/abs/alg-geom/9612010 | [
"alg-geom",
"math.AG"
] | alg-geom/9612010 | Wolfgang Ebeling | Wolfgang Ebeling | Strange duality, mirror symmetry, and the Leech lattice | LaTeX2e, 21 p. with 4 fig.; some corrections and additions | null | null | University of Hannover Preprint No. 279 | null | We give a survey on old and new results concerning Arnold's strange duality.
We show that most of the features of this duality continue to hold for the
extension of it discovered by C. T. C. Wall and the author. The results include
relations to mirror symmetry and the Leech lattice.
| [
{
"version": "v1",
"created": "Thu, 12 Dec 1996 14:21:16 GMT"
},
{
"version": "v2",
"created": "Thu, 12 Mar 1998 13:07:11 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Ebeling",
"Wolfgang",
""
]
] | alg-geom | \section*{Introduction}
More than 20 years ago, V.~I.~Arnold \cite{Arnold75} discovered a strange
duality
among the 14 exceptional unimodal hypersurface singularities. A beautiful
interpretation of this duality was given by H.~Pinkham \cite{Pinkham77} and
independently by I.~V.~Dolgachev and V.~V.~Nikulin \cite{DN77, ... |
1996-12-06T15:28:42 | 9612 | alg-geom/9612005 | en | https://arxiv.org/abs/alg-geom/9612005 | [
"alg-geom",
"math.AG"
] | alg-geom/9612005 | Ezra Getzler | Ezra Getzler | The semi-classical approximation for modular operads | 11 pages, amslatex-1.2 | null | null | MPI 96-145 | null | The semi-classical approximation is an explicit formula of mathematical
physics for the sum of Feynman diagrams with a single circuit.In this paper, we
study the same problem in the setting of modular operads (see dg-ga/9408003);
instead of being a number, the interaction at a vertex of valence n is an
S_n-module.
... | [
{
"version": "v1",
"created": "Fri, 6 Dec 1996 14:28:42 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Getzler",
"Ezra",
""
]
] | alg-geom | \subsection*{Acknowledgments}
I wish to thank the Department of Mathematics at the Universit\'e de
Paris-VII the Max-Planck-Institut f\"ur Mathematik in Bonn for their
hospitality during the inception and completion, respectively, of this
paper. I am grateful to D. Zagier for showing me the asymptotic expansion
of Cor... |
1997-09-04T21:14:16 | 9709 | alg-geom/9709004 | en | https://arxiv.org/abs/alg-geom/9709004 | [
"alg-geom",
"math.AG"
] | alg-geom/9709004 | Ravi Vakil | Ravi Vakil | Genus g Gromov-Witten invariants of Del Pezzo surfaces: Counting plane
curves with fixed multiple points | LaTeX2e | null | null | null | null | As another application of the degeneration methods of [V3], we count the
number of irreducible degree $d$ geometric genus $g$ plane curves, with fixed
multiple points on a conic $E$, not containing $E$, through an appropriate
number of general points in the plane. As a special case, we count the number
of irreducible... | [
{
"version": "v1",
"created": "Thu, 4 Sep 1997 19:13:49 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Vakil",
"Ravi",
""
]
] | alg-geom | \section{Introduction}
In this note, we count the number of irreducible degree $d$ geometric
genus $g$ plane curves, with fixed multiple points on a conic $E$, not
containing $E$, through an appropriate number of general points in the
plane. As a special case, we count the number of irreducible genus $g$
curves in an... |
1997-09-17T18:48:54 | 9709 | alg-geom/9709020 | en | https://arxiv.org/abs/alg-geom/9709020 | [
"alg-geom",
"math.AG"
] | alg-geom/9709020 | Vladimir Masek | Vladimir Masek (Washington Univ. in St. Louis) | Very ampleness of adjoint linear systems on smooth surfaces with
boundary | 22 pages, AMS-LaTeX 1.2 | null | null | null | null | Let M be a Q-divisor on a smooth surface over C. In this paper we give
criteria for very ampleness of the adjoint of the round-up of M. (Similar
results for global generation were given by Ein and Lazarsfeld and used in
their proof of Fujita's Conjecture in dimension 3.) In the last section we
discuss an example whic... | [
{
"version": "v1",
"created": "Wed, 17 Sep 1997 16:48:39 GMT"
}
] | 2016-08-30T00:00:00 | [
[
"Masek",
"Vladimir",
"",
"Washington Univ. in St. Louis"
]
] | alg-geom | \subsection*{Contents}
\begin{enumerate}
\item[0.] Introduction
\item[1.] Base-point-freeness
\item[2.] Separation of points
\item[3.] Separation of tangent directions
\item[4.] Example
\end{enumerate}
\subsection*{Notations}
\begin{tabbing}
99\=9999999999\=9999999999999999999999999999\kill
\>$\lceil \c... |
1997-09-04T21:13:34 | 9709 | alg-geom/9709003 | en | https://arxiv.org/abs/alg-geom/9709003 | [
"alg-geom",
"math.AG"
] | alg-geom/9709003 | Ravi Vakil | Ravi Vakil | Counting curves of any genus on rational ruled surfaces | LaTeX2e | null | null | null | null | In this paper we study the geometry of the Severi varieties parametrizing
curves on the rational ruled surface $\fn$. We compute the number of such
curves through the appropriate number of fixed general points on $\fn$, and the
number of such curves which are irreducible. These numbers are known as Severi
degrees; th... | [
{
"version": "v1",
"created": "Thu, 4 Sep 1997 19:13:10 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Vakil",
"Ravi",
""
]
] | alg-geom | \section{Introduction}
In this paper we study the geometry of the {\em Severi varieties}
parametrizing curves on the rational ruled surface ${\mathbb F}_n = \mathbb P
({\mathcal{O}}_{\mathbb P^1} \oplus {\mathcal{O}}_{\mathbb P^1}(n))$ ($n \ge 0$) in a given divisor
class. We compute the number of such curves through... |
1997-09-11T11:44:37 | 9709 | alg-geom/9709014 | fr | https://arxiv.org/abs/alg-geom/9709014 | [
"alg-geom",
"math.AG"
] | alg-geom/9709014 | Jean-Marc Drezet | Jean-Marc Dr\'ezet | Fibr\'es prioritaires g\'en\'eriques instables sur le plan projectif | LaTeX | null | null | null | null | The structure of the generic prioritary sheaf on the projective plane is
given, when it cannot be semi-stable
| [
{
"version": "v1",
"created": "Thu, 11 Sep 1997 09:42:14 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Drézet",
"Jean-Marc",
""
]
] | alg-geom | \section{Introduction}
Les faisceaux prioritaires sur \proj{2} ont \'et\'e
introduits par A. Hirschowitz et Y. Laszlo dans \cite{hi_la}. Rappelons qu'un
faisceau coh\'erent ${\cal E}$ sur \proj{2} est dit {\em prioritaire} s'il est sans
torsion et si \ \m{\mathop{\rm Ext}\nolimits^2({\cal E},{\cal E}(-1))=0}. Par exem... |
1997-09-26T22:13:44 | 9709 | alg-geom/9709030 | en | https://arxiv.org/abs/alg-geom/9709030 | [
"alg-geom",
"math.AG"
] | alg-geom/9709030 | Brent Gordon | B. Brent Gordon | A Survey of the Hodge Conjecture for Abelian Varieties | 68 pages, AMSTeX. To appear as Appendix B in the upcoming second
edition of "A Survey of the Hodge Conjecture" by James D. Lewis | null | null | null | null | We review what is known about the Hodge conjecture for abelian varieties,
with some emphasis on how Mumford-Tate groups have been applied to this
problem.
| [
{
"version": "v1",
"created": "Fri, 26 Sep 1997 20:13:44 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Gordon",
"B. Brent",
""
]
] | alg-geom | \chapter{\let\savedef@\chapter
\def\chapter##1{\let\chapter\savedef@
\leavevmode\hskip-\leftskip
\rlap{\vbox to\z@{\vss\centerline{\tenpoint
\frills@{CHAPTER\space\afterassignment\chapterno@
\global\chaptercount@=}%
##1\unskip}\baselineskip36pt\null}}\hskip\leftskip}%
\nofrillscheck\chapter}
\de... |
1997-09-11T17:31:29 | 9709 | alg-geom/9709011 | en | https://arxiv.org/abs/alg-geom/9709011 | [
"alg-geom",
"math.AG"
] | alg-geom/9709011 | Jonathan Fine | Jonathan Fine | Local-global intersection homology | LaTeX 2e. 28 pages. This paper defines new intersection homology
groups, that provide important new information | null | null | null | null | This paper defines new intersection homology groups. The basic idea is this.
Ordinary homology is locally trivial. Intersection homology is not. It may have
significant local cycles. A local-global cycle is defined to be a family of
such local cycles that is, at the same time, a global cycle. The motivating
problem i... | [
{
"version": "v1",
"created": "Wed, 10 Sep 1997 14:58:41 GMT"
},
{
"version": "v2",
"created": "Thu, 11 Sep 1997 15:31:29 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Fine",
"Jonathan",
""
]
] | alg-geom | \section{Introduction}
This paper defines new intersection homology groups. They record, in a
global way, local information about the singularities. They give rise to
new information, both globally and locally, and vanish on nonsingular
varieties. Such groups are required, to obtain a satisfactory
understanding of g... |
1997-09-12T23:10:33 | 9709 | alg-geom/9709016 | en | https://arxiv.org/abs/alg-geom/9709016 | [
"alg-geom",
"math.AG"
] | alg-geom/9709016 | James A. Carlson | Daniel Allcock, James A. Carlson, Domingo Toledo | A Complex Hyperbolic Structure for Moduli of Cubic Surfaces | Six pages, plain tex, available at http://www.math.utah.edu/~allcock | null | 10.1016/S0764-4442(97)82711-5 | null | null | We show that the moduli space M of marked cubic surfaces is biholomorphic to
the quotient by a discrete group generated by complex reflections of the
complex four-ball minus the reflection hyperplanes of the group. Thus M carries
a complex hyperbolic structure: an (incomplete) metric of constant holomorphic
sectional... | [
{
"version": "v1",
"created": "Fri, 12 Sep 1997 21:10:31 GMT"
}
] | 2009-10-30T00:00:00 | [
[
"Allcock",
"Daniel",
""
],
[
"Carlson",
"James A.",
""
],
[
"Toledo",
"Domingo",
""
]
] | alg-geom | \section{1. Main results}
To a (marked) cubic surface corresponds a (marked) cubic threefold defined as
the
triple cover of ${\Bbb P}^3$ ramified along the surface. The period map $f$ for
these threefolds
is defined on the moduli space $M$ of marked cubic surfaces and takes its
values in the
quotient of the unit bal... |
1997-09-10T21:18:41 | 9709 | alg-geom/9709013 | en | https://arxiv.org/abs/alg-geom/9709013 | [
"alg-geom",
"math.AG"
] | alg-geom/9709013 | Fernando Torres | Rainer Fuhrmann, Fernando Torres | On Weierstrass points and optimal curves | 22 pages, Latex 2e | Rend. Circ. Mat. Palermo Suppl. 51, (1998) 25--46 | null | null | null | We use Weierstrass Point Theory and Frobenius orders to prove the uniqueness
(up to isomorphism) of some optimal curves.
| [
{
"version": "v1",
"created": "Wed, 10 Sep 1997 19:18:20 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Fuhrmann",
"Rainer",
""
],
[
"Torres",
"Fernando",
""
]
] | alg-geom | \section{Preliminaries}\label{1}
In this section we summarize some background material concerning
Weierstrass Point Theory, Frobenius orders and a rational divisor arising
from the Zeta Function of a curve defined over a finite field.
\subsection{Weierstrass Point Theory}\label{1.1}
Here we repeat relevant material f... |
1997-09-02T15:27:01 | 9709 | alg-geom/9709001 | en | https://arxiv.org/abs/alg-geom/9709001 | [
"alg-geom",
"math.AG"
] | alg-geom/9709001 | Mikhail Zaidenberg | H. Flenner and M. Zaidenberg | Rational cuspidal plane curves of type (d, d-3) | 17 Pages. Latex | null | null | null | null | In the previous paper [E-print alg-geom/9507004] we classified the rational
cuspidal plane curves C with a cusp of multiplicity deg C - 2. In particular,
we showed that any such curve can be transformed into a line by Cremona
transformations. Here we do the same for the rational cuspidal plane curves C
with a cusp of... | [
{
"version": "v1",
"created": "Mon, 1 Sep 1997 19:10:44 GMT"
},
{
"version": "v2",
"created": "Tue, 2 Sep 1997 13:29:03 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Flenner",
"H.",
""
],
[
"Zaidenberg",
"M.",
""
]
] | alg-geom | \section*{Introduction}
Let $C \subset {\bf P}^2$ be a rational cuspidal curve;
that is, it has only irreducible singularities (called
{\it cusps}).
We say that $C$ is of type $(d,\,m)$ if $d =$deg$\,C$
is the degree and
$m = \max_{P \in {\rm Sing}\,C} \{$mult$_P C\}$ is the
maximal multiplicity
of the singular points... |
1997-09-30T07:13:24 | 9709 | alg-geom/9709033 | en | https://arxiv.org/abs/alg-geom/9709033 | [
"alg-geom",
"math.AG"
] | alg-geom/9709033 | Daisuke Matsushita | Daisuke Matsushita | On fibre space structures of a projective irreducible symplectic
manifold | null | null | null | null | null | In this note, we investigate fibre space structures of a projective
irreducible symplectic manifold. We prove that an 2n-dimensional projective
irreducible symplectic manifold admits only an n-dimensional fibration over a
Fano variety which has only Q-factorial log-terminal singularities and whose
Picard number is on... | [
{
"version": "v1",
"created": "Tue, 30 Sep 1997 05:13:24 GMT"
}
] | 2016-08-30T00:00:00 | [
[
"Matsushita",
"Daisuke",
""
]
] | alg-geom | \section{Introduction}
We first define an {\it irreducible symplectic manifold}.
\begin{defn}
A complex manifold $X$ is called {\it irreducible symplectic}
if $X$ satisfies the following three conditions:
\begin{enumerate}
\item $X$ is compact and K\"{a}hler.
\item $X$ is simply connected.
\item $H^{0}(X,\Omega^{... |
1997-09-25T09:48:39 | 9709 | alg-geom/9709027 | en | https://arxiv.org/abs/alg-geom/9709027 | [
"alg-geom",
"math.AG"
] | alg-geom/9709027 | Masahiko Saito | Shinobu Hosono, Masa-Hiko Saito, and Jan Stienstra | On Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3 folds | LaTeX Version 2.09, 36 pages. Submitted to The Proceedings of
Taniguchi Symposium 1997, "Integrable Systems and Algebraic Geometry,
Kobe/Kyoto" | null | null | null | null | In this paper, we verify a part of the Mirror Symmetry Conjecture for
Schoen's Calabi-Yau 3-fold, which is a special complete intersection in a toric
variety. We calculate a part of the prepotential of the A-model Yukawa
couplings of the Calabi-Yau 3-fold directly by means of a theta function and
Dedekind's eta funct... | [
{
"version": "v1",
"created": "Thu, 25 Sep 1997 07:48:37 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Hosono",
"Shinobu",
""
],
[
"Saito",
"Masa-Hiko",
""
],
[
"Stienstra",
"Jan",
""
]
] | alg-geom | \section{Introduction}
\label{intro}
Let $W$ be a generic complete intersection variety
in $\P1 \times \P2 \times \P2$ which is defined by two equations
of multi-degrees $(1, 3, 0)$ and $(1, 0, 3)$ respectively.
A generic $W$ is a non-singular Calabi-Yau 3-fold,
which we call {\em Schoen's
Calabi-Yau 3-fold}~\cit... |
1997-09-17T17:52:07 | 9709 | alg-geom/9709019 | en | https://arxiv.org/abs/alg-geom/9709019 | [
"alg-geom",
"math.AG"
] | alg-geom/9709019 | Vladimir Masek | Vladimir Masek (Washington Univ. in St. Louis) | Kawachi's invariant for normal surface singularities | 16 pages, AMS-LaTeX 1.2 | null | null | null | null | We study a useful numerical invariant of normal surface singularities,
introduced recently by T. Kawachi. Using this invariant, we give a quick proof
of the (well-known) fact that all log-canonical surface singularities are
either elliptic Gorenstein or rational (without assuming a priori that they are
Q-Gorenstein).... | [
{
"version": "v1",
"created": "Wed, 17 Sep 1997 15:51:59 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Masek",
"Vladimir",
"",
"Washington Univ. in St. Louis"
]
] | alg-geom | \subsection*{Contents}
\begin{enumerate}
\item[0.] Introduction
\item[1.] Kawachi's invariant and log-canonical singularities
\item[2.] A theorem of Reider type on normal surfaces with boundary
\end{enumerate}
\subsection*{Notations}
\begin{tabbing}
99\=9999999999\=9999999999999999999999999999\kill
\>$\lcei... |
1997-09-29T10:42:46 | 9709 | alg-geom/9709031 | en | https://arxiv.org/abs/alg-geom/9709031 | [
"alg-geom",
"math.AG"
] | alg-geom/9709031 | Wolf Barth | W. Barth | K3 Surfaces with Nine Cusps | LaTeX | null | null | null | null | By a K3-surface with nine cusps I mean a surface with nine isolated double
points A_2, but otherwise smooth, such that its minimal desingularisation is a
K3-surface. It is shown, that such a surface admits a cyclic triple cover
branched precisely over the cusps. This parallels the theorem of Nikulin, that
a K3-surfac... | [
{
"version": "v1",
"created": "Mon, 29 Sep 1997 08:42:46 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Barth",
"W.",
""
]
] | alg-geom | \section{Introduction}
If $E_1,...,E_{16}$ are 16 disjoint, smooth curves on a $K3$-surface
$X$ then the divisor $\sum_1^{16} E_i$ is divisible by $2$ in
$Pic(X)$. This was observed by V.V. Nikulin [N]. Equivalently: If
$\bar{X}$ is the surface obtained from $X$ by blowing
down the 16 rational curves to nodes $e_i \in... |
1997-09-15T22:55:44 | 9709 | alg-geom/9709017 | en | https://arxiv.org/abs/alg-geom/9709017 | [
"alg-geom",
"math.AG"
] | alg-geom/9709017 | Yavor Markov | Y. Markov, V. Tarasov, A. Varchenko | The Determinant of a Hypergeometric Period Matrix | 21 pages, no figures, LaTeX2e | null | null | null | null | We consider a function $U=e^{-f_0}\prod_j^N f_j^{\alpha_j}$ on a real affine
space, here $f_0,..,f_N$ are linear functions, $\alpha_1, ...,\alpha_N$ complex
numbers. The zeros of the functions $f_1, ..., f_N$ form an arrangement of
hyperplanes in the affine space. We study the period matrix of the
hypergeometric inte... | [
{
"version": "v1",
"created": "Mon, 15 Sep 1997 20:51:53 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Markov",
"Y.",
""
],
[
"Tarasov",
"V.",
""
],
[
"Varchenko",
"A.",
""
]
] | alg-geom | \section{Introduction}
The Euler beta function is an alternating product of Euler gamma functions,
\begin{equation}\label{2}
B (\alpha, \beta)\,=\, {\Gamma (\alpha)\,\Gamma (\beta)
\over
\Gamma (\alpha + \beta)}
\end{equation}
where the
Euler gamma and beta functions are defined by
\begin{equation}\label{1}
\Gamma (... |
1997-09-10T17:43:13 | 9709 | alg-geom/9709012 | en | https://arxiv.org/abs/alg-geom/9709012 | [
"alg-geom",
"math.AG"
] | alg-geom/9709012 | Richard Earl | Richard Earl and Frances Kirwan | The Pontryagin rings of moduli spaces of arbitrary rank holomorphic
bundles over a Riemann surface | AMS-Latex, 15 pages, no figures | null | null | null | null | The cohomology of the moduli spaces of stable bundles M(n,d), of coprime rank
n and degree d, over a Riemann surface (of genus g > 1) have been intensely
studied over the past three decades. We prove in this paper that the Pontryagin
ring of M(n,d) vanishes in degrees above 2n(n-1)(g-1) and that this bound is
strict ... | [
{
"version": "v1",
"created": "Wed, 10 Sep 1997 15:42:31 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Earl",
"Richard",
""
],
[
"Kirwan",
"Frances",
""
]
] | alg-geom | \section{Introduction}
The cohomology of ${\cal M}(n,d)$, the moduli space of stable holomorphic
bundles of coprime rank $n$ and degree $d$ and fixed determinant,
over a Riemann surface
$\Sigma$ of genus $g \geq 2$, has been widely studied and from a wide
range of approaches. Narasimhan and Seshadri \cite{NS}
original... |
1997-09-30T15:36:07 | 9709 | alg-geom/9709034 | en | https://arxiv.org/abs/alg-geom/9709034 | [
"alg-geom",
"math.AG",
"math.CO"
] | alg-geom/9709034 | Frank Sottile | Nantel Bergeron (York University, Toronto) and Frank Sottile
(University of Toronto) | Skew Schubert functions and the Pieri formula for flag manifolds | 24 pages, LaTeX 2e, with epsf.sty | Trans. Amer. Math. Soc., 354 No. 2, (2002), 651-673 | 10.1090/S0002-9947-01-02845-8 | MSRI 1997-096 | null | We show the equivalence of the Pieri formula for flag manifolds and certain
identities among the structure constants, giving new proofs of both the Pieri
formula and of these identities. A key step is the association of a symmetric
function to a finite poset with labeled Hasse diagram satisfying a symmetry
condition.... | [
{
"version": "v1",
"created": "Tue, 30 Sep 1997 13:35:57 GMT"
}
] | 2016-11-08T00:00:00 | [
[
"Bergeron",
"Nantel",
"",
"York University, Toronto"
],
[
"Sottile",
"Frank",
"",
"University of Toronto"
]
] | alg-geom | \section*{Introduction}
A fundamental open problem in the theory of Schubert
polynomials is to find an analog of the Littlewood-Richardson
rule.
By this, we mean a bijective description of the structure
constants for the ring of polynomials with respect to its basis of Schubert
polynomials.
Such a rule would express t... |
1997-09-09T21:32:23 | 9709 | alg-geom/9709010 | en | https://arxiv.org/abs/alg-geom/9709010 | [
"alg-geom",
"math.AG"
] | alg-geom/9709010 | Yuri Tschinkel | Matthias Strauch and Yuri Tschinkel | Height zeta functions of toric bundles over flag varieties | 64 pages, LaTeX | null | null | null | null | We investigate analytic properties of height zeta functions of toric bundles
over flag varieties.
| [
{
"version": "v1",
"created": "Tue, 9 Sep 1997 19:29:16 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Strauch",
"Matthias",
""
],
[
"Tschinkel",
"Yuri",
""
]
] | alg-geom | \section{Introduction}
\label{1}
\subsection*
\noindent
{\bf 1.1}\hskip 0,5cm
Let $X$ be a nonsingular projective algebraic variety over a number field
$F$. Let ${\cal L}=\left(L, (\|\cdot\|_v)_v\right)$ be a metrized line
bundle on $X$, i.e., a line bundle $L$ together with a family of
$v$-adic metrics, where $... |
1997-09-16T21:14:56 | 9709 | alg-geom/9709018 | en | https://arxiv.org/abs/alg-geom/9709018 | [
"alg-geom",
"math.AG"
] | alg-geom/9709018 | Lakshmibai | V. Lakshmibai and Peter Magyar | Degeneracy Schemes and Schubert Varieties | 16 pp, Northeastern University, Latex | null | null | null | null | A result of Zelevinsky states that an orbit closure in the space of
representations of the equioriented quiver of type $A_h$ is in bijection with
the opposite cell in a Schubert variety of a partial flag variety $SL(n)/Q$. We
prove that Zelevinsky's bijection is a scheme-theoretic isomorphism, which
shows that the un... | [
{
"version": "v1",
"created": "Tue, 16 Sep 1997 19:16:12 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Lakshmibai",
"V.",
""
],
[
"Magyar",
"Peter",
""
]
] | alg-geom | \section{Zelevinsky's bijection}
\subsection{Quiver varieties}
Fix an $h$-tuple of non-negative integers
${\bf n} = (n_1,\ldots,n_h)$
and a list of vector spaces $V_1,\ldots, V_h$
over an arbitrary field ${\bf k}$
with respective dimensions $n_1,\ldots,n_h$.
Define the {\it variety of quiver representations}
(of dime... |
1997-09-29T19:35:02 | 9709 | alg-geom/9709032 | fr | https://arxiv.org/abs/alg-geom/9709032 | [
"alg-geom",
"math.AG"
] | alg-geom/9709032 | Laurent Evain | L. Evain | Dimension of linear systems: a combinatorial and differential approach | 17 pages, in french, also available at
http://193.49.162.129/~evain/home.html | null | null | UA 45 | null | We give upper-bounds for the dimension of some linear systems. The theorem
improves the differential Horace method introduced by Alexander-Hirschowitz,
and was conjectured by Simpson. Possible applications are the calculus of the
dimension of linear systems of hypersurfaces in a projective space $\PP^n$ with
generica... | [
{
"version": "v1",
"created": "Mon, 29 Sep 1997 17:35:02 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Evain",
"L.",
""
]
] | alg-geom | \section{Introduction par un exemple}
Consid\'erons le syst\`eme lin\'eaire ${\cal L}_t$ des courbes projectives
planes de degr\'e $d$ passant par trois points fixes
$p_1,p_2,p_3$ et par un point $p_4(t)$ avec multiplicit\'es respectives
$m_1,m_2,m_3$ et $m_4$. Supposons que
$p_1,p_2,p_3$ soient align\'es sur une... |
1997-09-25T16:01:03 | 9709 | alg-geom/9709028 | en | https://arxiv.org/abs/alg-geom/9709028 | [
"alg-geom",
"math.AG"
] | alg-geom/9709028 | Karin Smith | Edward Bierstone and Pierre D. Milman (University of Toronto) | Resolution of Singularities | 45 pages, 7 Postscript figures, LATEX. To appear in Current
Developments in Several Complex Variables, MSRI Proceedings, ed. M. Schneider
and Y.-T. Siu, Cambridge University Press | null | null | null | null | This article is an exposition of an elementary constructive proof of
canonical resolution of singularities in characteristic zero, presented in
detail in Invent. Math. 128 (1997), 207-302. We define a new local invariant
and get an algorithm for canonical desingularization by successively blowing up
its maximum loci.... | [
{
"version": "v1",
"created": "Thu, 25 Sep 1997 14:00:53 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Bierstone",
"Edward",
"",
"University of Toronto"
],
[
"Milman",
"Pierre D.",
"",
"University of Toronto"
]
] | alg-geom | \section{Introduction}
Resolution of singularities has a long history that goes back
to Newton in the case of plane curves.
For higher-dimensional singular spaces, the problem was formulated
toward the end of the last century, and it was solved in
general, for algebraic varieties defined over fields of characteristic
... |
1997-09-06T00:33:58 | 9709 | alg-geom/9709007 | en | https://arxiv.org/abs/alg-geom/9709007 | [
"alg-geom",
"math.AG"
] | alg-geom/9709007 | Ravi Vakil | Ravi Vakil | The enumerative geometry of rational and elliptic curves in projective
space | LaTeX2e, 95 pages with 18 figures | null | null | null | null | We study the geometry of varieties parametrizing degree d rational and
elliptic curves in P^n intersecting fixed general linear spaces and tangent to
a fixed hyperplane H with fixed multiplicities along fixed general linear
subspaces of H. As an application, we derive recursive formulas for the number
of such curves ... | [
{
"version": "v1",
"created": "Fri, 5 Sep 1997 22:32:50 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Vakil",
"Ravi",
""
]
] | alg-geom |
\section{Introduction}
\label{intro}
In this article, we study the geometry of varieties (over $\mathbb{C}$)
parametrizing degree $d$ rational and elliptic curves in $\mathbb P^n$
intersecting fixed general linear spaces and tangent to a fixed hyperplane
$H$ with fixed multiplicities along fixed general... |
1997-09-04T10:37:48 | 9709 | alg-geom/9709002 | en | https://arxiv.org/abs/alg-geom/9709002 | [
"alg-geom",
"math.AG"
] | alg-geom/9709002 | Vicente Munoz Velazquez | Vicente Mu\~noz | Wall-crossing formulae for algebraic surfaces with $q>0$ | Latex2e, 20 pages | null | null | null | null | We extend the ideas of Friedman and Qin (Flips of moduli spaces and
transition formulae for Donaldson polynomial invariants of rational surfaces)
to find the wall-crossing formulae for the Donaldson invariants of algebraic
surfaces with geometrical genus zero, positive irregularity and anticanonical
divisor effective... | [
{
"version": "v1",
"created": "Thu, 4 Sep 1997 09:38:04 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Muñoz",
"Vicente",
""
]
] | alg-geom | \section{Introduction}
\label{sec:intro}
The Donaldson invariants of a smooth oriented $4$-manifold $X$
depend by definition on a Riemannian metric $g$. In the
case $b^+>1$ they however turn out to be independent of $g$. When
$b^+=1$, they depend on $g$ through a structure of walls and chambers, that we
recall brief... |
1997-09-26T19:11:48 | 9709 | alg-geom/9709029 | en | https://arxiv.org/abs/alg-geom/9709029 | [
"alg-geom",
"hep-th",
"math.AG"
] | alg-geom/9709029 | Robert Friedman | Robert Friedman, John W. Morgan, and Edward Witten | Vector Bundles over Elliptic Fibrations | 101 pages, AMS-TeX, amsppt style | null | null | null | null | This paper gives various methods for constructing vector bundles over
elliptic curves and more generally over families of elliptic curves. We
construct universal families over generalized elliptic curves via spectral
cover methods and also by extensions, and then give a relative version of the
construction in familie... | [
{
"version": "v1",
"created": "Fri, 26 Sep 1997 17:11:47 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Friedman",
"Robert",
""
],
[
"Morgan",
"John W.",
""
],
[
"Witten",
"Edward",
""
]
] | alg-geom | \section{Introduction}
Let $\pi \: Z \to B$ be an elliptic fibration with a section. The goal of
this paper is to study holomorphic vector bundles over $Z$. We are mainly
concerned with vector bundles $V$ with trivial determinant, or more
generally such that $\det V$ has trivial restriction to each fiber, so that
$\d... |
1998-12-11T18:24:46 | 9709 | alg-geom/9709025 | en | https://arxiv.org/abs/alg-geom/9709025 | [
"alg-geom",
"math.AG"
] | alg-geom/9709025 | Christoph Sorger | Christoph Sorger | On Moduli of G-bundles over Curves for exceptional G | Plain TeX, 6 p. Reason for resubmission: proof of main result has
been simplified | null | null | null | null | Let $G$ be a simple and simply connected complex Lie group, ${\goth{g}}$ its
Lie algebra. I remove the restriction ``$G$ is of classical type or $G_2$''
made on $G$ in the papers of Beauville, Laszlo and myself [L-S] and [B-L-S] on
the moduli of principal G-bundles over a curve. As I will just "patch" the
missing tec... | [
{
"version": "v1",
"created": "Mon, 22 Sep 1997 20:56:23 GMT"
},
{
"version": "v2",
"created": "Thu, 2 Oct 1997 09:18:16 GMT"
}
] | 2009-09-25T00:00:00 | [
[
"Sorger",
"Christoph",
""
]
] | alg-geom | \section{Introduction}
\par\hskip 1truecm\relax Let $G$ be a simple and simply connected complex Lie group, $\g$ its Lie
algebra. In the following, I remove the restriction ``$G$ is of classical type
or
$G_2$'' made on $G$ in the papers of Beauville, Laszlo and
myself \cite{L-S:verlinde},\cite{B-L-S:picard}
on the mod... |
1994-08-24T22:26:05 | 9408 | alg-geom/9408007 | en | https://arxiv.org/abs/alg-geom/9408007 | [
"alg-geom",
"math.AG"
] | alg-geom/9408007 | Caryn Werner | Caryn Werner | A surface of general type with \( p_g =q =0, K^2 =1 \) | 13 pages, AMS-LaTex version 1.1 | null | null | null | null | We construct a surface of general type with invariants \( \chi = K^2 = 1 \)
and torsion group \( \Bbb{Z}/{2} \). We use a double plane construction by
finding a plane curve with certain singularities, resolving these, and taking
the double cover branched along the resulting smooth curve.
| [
{
"version": "v1",
"created": "Wed, 24 Aug 1994 20:25:38 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Werner",
"Caryn",
""
]
] | alg-geom | \section{Introduction}
In this paper we construct a
minimal surface \(X\) of general type with
\(\rm{{p}_{g}}=0,\rm{q}=0, {K}^{2}=1,\)
and \( \operatorname{Tors} X \cong \Bbb{Z}/{2}\).
In \cite{Ca}, Campedelli noted that if a degree ten
plane curve could be found having certain singularities,
a double plane constructio... |
1994-08-04T16:05:34 | 9408 | alg-geom/9408001 | en | https://arxiv.org/abs/alg-geom/9408001 | [
"alg-geom",
"math.AG"
] | alg-geom/9408001 | Daniel Huybrechts | Lothar Goettsche, Daniel Huybrechts | Hodge numbers of moduli spaces of stable bundles on K3 surfaces | 12 pages, latex | null | null | null | null | We show that the Hodge numbers of the moduli space of stable rank two sheaves
with primitive determinant on a K3 surface coincide with the Hodge numbers of
an appropriate Hilbert scheme of points on the K3 surface. The precise result
is: Theorem: Let $X$ be a K3 surface, $L$ a primitive big and nef line bundle
and $H... | [
{
"version": "v1",
"created": "Thu, 4 Aug 1994 15:02:20 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Goettsche",
"Lothar",
""
],
[
"Huybrechts",
"Daniel",
""
]
] | alg-geom | \section{A special case}
In this section we prove the theorem in the case that ${\rm Pic }(X)=\hbox{\sym \char '132}\cdot
L$ and $c_2=\frac{L^2}{2}+3$.
{\small\subsection{ The birational correspondence to the Hilbert scheme}}
Throughout this section we will assume that the Picard group is generated by
an ample line bu... |
1994-08-09T11:21:15 | 9408 | alg-geom/9408002 | en | https://arxiv.org/abs/alg-geom/9408002 | [
"alg-geom",
"math.AG"
] | alg-geom/9408002 | Luca Barbieri-Viale | Luca Barbieri-Viale | ${\cal H}$-cohomologies versus algebraic cycles | 51 pages, LaTeX 2.09 | Math. Nachr. 184 (1997), 5-57 | null | null | null | Global intersection theories for smooth algebraic varieties via products in
{\it appropriate}\, Poincar\'e duality theories are obtained. We assume given a
(twisted) cohomology theory $H^*$ having a cup product structure and we let
consider the ${\cal H}$-cohomology functor $X\leadsto H^{\#}_{Zar}(X,{\cal
H}^*)$ wher... | [
{
"version": "v1",
"created": "Mon, 8 Aug 1994 14:29:25 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Barbieri-Viale",
"Luca",
""
]
] | alg-geom | \section{Introduction}
After Quillen's proof of the Gersten conjecture (see
\cite{Q}), for algebraic regular schemes, a natural
approach to the theory of algebraic cycles appears to be
by dealing with the ``formalism'' associated to (local)
higher $K$-theory, as it is manifestly expressed by the
work of Bloch and Gill... |
1994-08-24T11:31:56 | 9408 | alg-geom/9408006 | en | https://arxiv.org/abs/alg-geom/9408006 | [
"alg-geom",
"math.AG"
] | alg-geom/9408006 | Serge M. L'vovsky | S.L'vovsky | On Landsberg's criterion for complete intersections | 4 pages, LaTeX 2.09 | null | null | null | null | In his preprint ``Differential-Geometric Characterizations of Complete
Intersections'' (alg-geom/9407002), J.M.Landsberg introduces an elementary
characterization of complete intersections. The proof of this criterion uses
the method of moving frames. The aim of this note is to present an elementary
proof of Landsber... | [
{
"version": "v1",
"created": "Wed, 24 Aug 1994 08:43:07 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"L'vovsky",
"S.",
""
]
] | alg-geom | \section*{Introduction}
In his preprint~\cite{Lan}, J.M.~Landsberg introduces an
elementary characterization of complete intersections
(Proposition~1.2 in \cite{Lan}). The proof of this proposition
uses the method of moving frames. The aim of this note is to
present an elementary proof of Landsberg's criterion that is
... |
1994-08-29T10:45:38 | 9408 | alg-geom/9408008 | en | https://arxiv.org/abs/alg-geom/9408008 | [
"alg-geom",
"math.AG"
] | alg-geom/9408008 | Robert W. Berger | Robert W. Berger | Various Notions of Associated Prime Ideals | 27 pages, AMS-LaTeX 1.1 | null | null | null | null | Three notions of associated prime ideals, which are equivalent in the
noetherian case but differ in the non notherian case, are discussed. Examples
illustrate the scope of the notions.
| [
{
"version": "v1",
"created": "Mon, 29 Aug 1994 08:37:20 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Berger",
"Robert W.",
""
]
] | alg-geom | \section*{Introduction}
In the theory of modules over commutative rings there are several
possibilities of defining associated prime ideals.
The usual definition of an associated prime ideal $\frak p$ for a
module $M$ is that $\frak p$ is the annihilator of an element of $M$.
In \cite{Bourbaki-Alg-Comm-4} \S 1 exercise... |
1993-01-06T16:06:57 | 9301 | alg-geom/9301003 | en | https://arxiv.org/abs/alg-geom/9301003 | [
"alg-geom",
"math.AG"
] | alg-geom/9301003 | null | Marc Coppens and Takao Kato | Non-trivial Linear Systems on Smooth Plane Curves | 15 pages, LaTeX 2.09 | null | null | null | null | Let $C$ be a smooth plane curve of degree $d$ defined over an algebraically
closed field $k$. A base point free complete very special linear system $g^r_n$
on $C$ is trivial if there exists an integer $m\ge 0$ and an effective divisor
$E$ on $C$ of degree $md-n$ such that $g^r_n=|mg^2_d-E|$ and
$r=(m^2+3m)/2-(md-n)$.... | [
{
"version": "v1",
"created": "Wed, 6 Jan 1993 15:15:44 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Coppens",
"Marc",
""
],
[
"Kato",
"Takao",
""
]
] | alg-geom | \section{Introduction}
Let $C$ be a smooth plane curve of degree $d$ defined over an
algebraically closed field $k$. In \cite{noether}, while studying space
curves, Max Noether considered the following question. For
$n\in{\bbb Z}_{\ge 1}$ find $\ell (n)\in{\bbb Z}_{\ge 0}$ such that there
exists a linear system $g^{... |
1993-02-01T20:50:11 | 9301 | alg-geom/9301006 | en | https://arxiv.org/abs/alg-geom/9301006 | [
"alg-geom",
"hep-th",
"math.AG"
] | alg-geom/9301006 | null | Sheldon Katz | Rational curves on Calabi-Yau manifolds: verifying predictions of Mirror
Symmetry | 12 pages, LaTeX (Replaced version corrects an error in the formula
for bundle $B'$ on page 5, and changes the order of some entries in tables 2
and 3 for compatibility with the associated computer file) | null | null | OSU Math 1992-3 | null | Mirror symmetry, a phenomenon in superstring theory, has recently been used
to give tentative calculations of several numbers in algebraic geometry. In
this paper, the numbers of lines and conics on various hypersurfaces which
satisfy certain incidence properties are calculated, and shown to agree with
the numbers pr... | [
{
"version": "v1",
"created": "Wed, 27 Jan 1993 23:05:22 GMT"
},
{
"version": "v2",
"created": "Mon, 1 Feb 1993 19:39:30 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Katz",
"Sheldon",
""
]
] | alg-geom | \section*{}
Recently, mirror symmetry, a phenomenon in superstring theory,
has been used to give tentative calculations of several numbers
in algebraic geometry \nolinebreak\footnote{See the papers in \cite{yau} for
general background on mirror symmetry.}. This yields predictions for the
number of rational
curves of a... |
1993-03-08T22:08:32 | 9301 | alg-geom/9301007 | en | https://arxiv.org/abs/alg-geom/9301007 | [
"alg-geom",
"math.AG"
] | alg-geom/9301007 | Zhi-Jie Chen | Zhi-Jie Chen | Bounds of automorphism groups of genus 2 fibrations | 30 pages, LaTeX2.09 | null | null | null | null | For a complex surface of general type with a relatively minimal genus 2
fibration, the bounds of the orders of the automorphism group of the fibration,
of its abelian subgroups and of its cyclic subgroups are determined as linear
functions of $c^2_1$. Most of them are the best.
| [
{
"version": "v1",
"created": "Fri, 29 Jan 1993 21:30:56 GMT"
},
{
"version": "v2",
"created": "Mon, 8 Mar 1993 21:07:47 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Chen",
"Zhi-Jie",
""
]
] | alg-geom | \section{Preliminaries}
The surfaces with genus 2 pencils have been largely studied by many authors.
The facts we needed in this paper mostly appeared in [3, 6, 9, 10]. In
particular, Xiao's book \cite{X3} gave a systematic description of the
properties of genus 2 fibrations which are just what we needed here.
Unfortu... |
1993-01-20T12:50:02 | 9301 | alg-geom/9301004 | en | https://arxiv.org/abs/alg-geom/9301004 | [
"alg-geom",
"math.AG"
] | alg-geom/9301004 | Sorin Popescu | A. Aure, W. Decker, K. Hulek, S. Popescu, K. Ranestad | The Geometry of Bielliptic Surfaces in P^4 | 28 pages. AMSLaTeX 1.1 | null | null | null | null | In 1988 Serrano \cite{Ser}, using Reider's method, discovered a minimal
bielliptic surface in $\PP^4$. Actually he showed that there is a unique family
of such surfaces and that they have degree 10 and sectional genus 6. In this
paper we describe, among other things, the geometry of the embedding of the
minimal biell... | [
{
"version": "v1",
"created": "Wed, 20 Jan 1993 11:44:54 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Aure",
"A.",
""
],
[
"Decker",
"W.",
""
],
[
"Hulek",
"K.",
""
],
[
"Popescu",
"S.",
""
],
[
"Ranestad",
"K.",
""
]
] | alg-geom | \section{Heisenberg invariants on $\Bbb P^2$}
Here we collect some well-known facts about invariants of the
Schr\"odinger representation of $H_3$, the Heisenberg group of level
$3$. Let $x_0,x_1,x_2$ be a basis of
$\mathrm H^\circ(\cal O_{\Bbb P^2}(1))$ and consider the dual of the
Schr\"odinger representation of $H_3... |
1993-04-09T17:12:04 | 9303 | alg-geom/9303005 | en | https://arxiv.org/abs/alg-geom/9303005 | [
"alg-geom",
"math.AG"
] | alg-geom/9303005 | Roberto Paoletti | Roberto Paoletti | Free pencils on divisors | 18 pages, amslatex | null | null | null | null | Let X be a smooth projective variety defined over an algebraically closed
field, and let Y in X be a reduced and irreducible ample divisor in X. We give
a numerical sufficient condition for a base point free pencil on $Y$ to be the
restriction of a base point free pencil on $X$. This result is then extended to
famili... | [
{
"version": "v1",
"created": "Sun, 28 Mar 1993 21:29:31 GMT"
},
{
"version": "v2",
"created": "Fri, 9 Apr 1993 15:12:29 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Paoletti",
"Roberto",
""
]
] | alg-geom | \section{\bf {Introduction}}
In algebraic geometry, it is rather typical that the
embedding of a variety $Y$ in another variety
$X$ forces strong constraints on the existence of free linear
series on $Y$.
For example, a classical result in plane curve theory states
that
the gonality of a smooth plane curve of deg... |
1993-03-28T20:31:54 | 9303 | alg-geom/9303004 | en | https://arxiv.org/abs/alg-geom/9303004 | [
"alg-geom",
"math.AG"
] | alg-geom/9303004 | Ron Donagi | Ron Donagi and Loring W. Tu | Theta Functions for $\SL(n)$ versus $\GL(n)$ | 10 pages, Latex | null | null | null | null | Over a smooth complex projective curve $C$ of genus $g$ let $\M (n,d)$ be the
moduli space of semistable bundles of rank $n$ and degree $d$ on $C$, and $\SM
(n,L)$, the moduli space of those bundles whose determinant is isomorphic to a
fixed line bundle $L$ over $C$. Let $\theta_F$ and $\theta$ be theta bundles
over ... | [
{
"version": "v1",
"created": "Sun, 28 Mar 1993 18:31:37 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Donagi",
"Ron",
""
],
[
"Tu",
"Loring W.",
""
]
] | alg-geom | \section{Theta bundles}
\label{bundles}
We recall here
the definitions of the theta bundles on a fixed-determinant moduli
space and on a full moduli space.
Our definitions are slightly different from but equivalent to those in
\cite{drezet-narasimhan}.
For $L \in {\rm Pic} ^d (C)$, the Picard group of ${\cal SM} :=... |
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