The geometry of Siegel modular varieties

Details The geometry of Siegel modular varieties The geometry of Siegel modular varieties

1998-10-27

arxiv.org/abs/math/9810153v2

Mathematics

Algebraic Geometry

66 pages, LaTeX, xyfig. References updated, section VI.2 rewritten and updated, other minor corrections

Scientific paper

This is a survey article about Siegel modular varieties over the complex numbers. It is written mostly from the point of view of moduli of abelian varieties, especially surfaces. We cover compactification of Siegel modular varieties; classification of the compactified varieties by Kodaira dimension, etc.; moduli of abelian surfaces and especially applications of the lifting of Jacobi forms to modular forms; projective models of some special Siegel modular 3-folds; non-principally polarized abelian surfaces; and constructing degenerating families of abelian varieties.

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