Compactifying Moduli Spaces for Abelian Varieties

  • Martin C. Olsson

Part of the Lecture Notes in Mathematics book series (LNM, volume 1958)

Table of contents

About this book

Introduction

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.

Keywords

Abelian varieties Abelian variety Canon Compactification Moduli Prime Volume algebra compactifications construction geometry group logarithm techniques

Authors and affiliations

  • Martin C. Olsson
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-70519-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-70518-5
  • Online ISBN 978-3-540-70519-2
  • Series Print ISSN 0075-8434
  • About this book