Compactifying moduli spaces for Abelian varieties / Martin C. Olsson.

Format:

Book

Author/Creator:

Olsson, Martin C.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 1958.

Lecture notes in mathematics, 0075-8434 ; 1958

Language:

English

Subjects (All):

Abelian varieties.

Moduli theory.

Physical Description:

vi, 278 pages : illustrations ; 23 cm.

Place of Publication:

Berlin : Springer, [2008]

Summary:

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.

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.

Notes:

Includes bibliographical references (pages [273]-275) and index.

ISBN:

9783540705185

354070518X

OCLC:

232976387