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Compactifying Moduli Spaces for Abelian Varieties

  • Book
  • © 2008

Overview

Authors:
  1. Martin C. Olsson

    1. Department of Mathematics, University of California, Berkeley, USA

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Part of the book series: Lecture Notes in Mathematics (LNM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VII
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  2. Introduction

    Pages 1-5

  3. A Brief Primer on Algebraic Stacks

    Pages 7-29

  4. Preliminaries

    Pages 31-55

  5. Moduli of Broken Toric Varieties

    Pages 57-83

  6. Moduli of Principally Polarized Abelian Varieties

    Pages 85-134

  7. Moduli of Abelian Varieties with Higher Degree Polarizations

    Pages 135-230

  8. Level Structure

    Pages 231-271

  9. Back Matter

    Pages 273-278
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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

  • Department of Mathematics, University of California, Berkeley, USA

    Martin C. Olsson

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

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