Compactifying Moduli Spaces for Abelian Varieties pdf epub mobi txt 电子书下载 2025

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出版者:

作者:Olsson, Martin C.

出品人:

页数:278

译者:

出版时间:

价格:$ 79.04

装帧:

isbn号码:9783540705185

丛书系列:Lecture Notes in Mathematics

图书标签:

数学
Abelian varieties
Moduli spaces
Compactification
Algebraic geometry
Complex analysis
Arithmetic geometry
Scheme theory
Hodge theory
Period domains
Mixed Hodge modules

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具体描述

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.