Contents

1 Introduction and Summary

2 Dudas-Palti Relations and General Implications
2.1 Anomaly Cancellation
2.2 'Uniqueness' of U(1)B-L
2.3 U(1)PQ Symmetries and Exotics

3 Spectral Cover and Dudas-Palti Relations
3.1 Calabi-Yau 4-folds and Higgs Bundles
3.2 U(1) Symmetries and Spectral Cover Models
3.3 Technical Matters and Matter Curves
3.4 Dudas-Palti Relations
3.5 Deriving the Dudas-Palti Relations for Spectral Cover Models
3.6 Survey