ENGLISH

Compactifying Moduli Spaces for Abelian Varieties

By Martin C. Olsson (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2008
ISBN
354070518X, 9783540705185
DOI
10.1007/978-3-540-70519-2
Language
english
Format
PDF
Filesize
2 MB (2409925 bytes)
Series
Lecture Notes in Mathematics 1958
Edition
1
Pages
286\286
Time added
2011-06-04 13:46:07
Algebraic Geometry

Description

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.

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