Lecture Notes in Mathematics

Compactifying Moduli Spaces for Abelian Varieties

Authors: Olsson, Martin C.

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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)


Table of contents (7 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-70519-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-540-70518-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Compactifying Moduli Spaces for Abelian Varieties
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1958
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-70519-2
DOI
10.1007/978-3-540-70519-2
Softcover ISBN
978-3-540-70518-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 286
Number of Illustrations and Tables
1 b/w illustrations
Topics