Compactifying moduli spaces for abelian varieties

Martin C. Olsson (auth.)354070518X, 9783540705185

This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.

Table of contents :
Front Matter….Pages I-VII
Introduction….Pages 1-5
A Brief Primer on Algebraic Stacks….Pages 7-29
Preliminaries….Pages 31-55
Moduli of Broken Toric Varieties….Pages 57-83
Moduli of Principally Polarized Abelian Varieties….Pages 85-134
Moduli of Abelian Varieties with Higher Degree Polarizations….Pages 135-230
Level Structure….Pages 231-271
Back Matter….Pages 273-278