Compactifying Moduli Spaces for Abelian Varieties

2008
ISBN: 978-3-540-70518-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1958, 286 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 452 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Olsson, Martin C.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Inhaltsverzeichnis

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.