Contents

1. Introduction: The Decomposition Problem.
2. The Three ‘Pure’ Geometries
3. Geometric Orbifolds
4. Orbifold Base of a Fibration
5. Orbifold Additivity
6. Special Orbifolds
7. The Core
8. The Decomposition of the Core
9. Orbifold Rational Curves
10. Some Relationships to LMMP and Abundance Conjecture.
11. Some Conjectures
12. Special Versus Weakly Special Manifolds
13. Classical Versus ‘Non-Classical’ Multiplicities
14. An Orbifold Version of Mordell’s Conjecture