Compactifying moduli spaces for Abelian varieties /

Compactifying moduli spaces for Abelian varieties /

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Bibliographic Details
Author / Creator:	Olsson, Martin C.
Imprint:	Berlin : Springer, ©2008.
Description:	1 online resource (vi, 278 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1958 Lecture notes in mathematics (Springer-Verlag) ; 1958.
Subject:	Abelian varieties. Moduli theory. Abelian varieties. Moduli theory.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11069732

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ISBN:	9783540705192 3540705198 9783540705185 354070518X
Notes:	Includes bibliographical references (pages 273-275) and index. Print version record.
Summary:	Annotation 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.
Other form:	Print version: Olsson, Martin C. Compactifying moduli spaces for Abelian varieties. Berlin : Springer, ©2008 9783540705185

Table of Contents:

Introduction
A brief primer on algebraic stacks
Preliminaries
Moduli of broken toric varieties
Moduli of principally polarized Abelian varieties
Moduli of Abelian varieties with higher degree polarizations
Level structure.