Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM)
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Table of contents (7 chapters)
Keywords
About this book
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.
Reviews
From the reviews:
"No doubt, the work presented in this research monograph is a fundamental contribution to the compactification theory of moduli spaces in general, and of moduli spaces for abelian varieties in particular. … the present monograph is written in a very lucid, comprehensive, largely self-contained and enlightening style, including numerous additional remarks and hints." (Werner Kleinert, Zentralblatt MATH, Vol. 1165, 2009)
Authors and Affiliations
Bibliographic Information
Book Title: Compactifying Moduli Spaces for Abelian Varieties
Authors: Martin C. Olsson
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-70519-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Softcover ISBN: 978-3-540-70518-5Published: 25 August 2008
eBook ISBN: 978-3-540-70519-2Published: 25 July 2008
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 286
Number of Illustrations: 1 b/w illustrations
Topics: Algebraic Geometry