Compactifying Moduli Spaces for Abelian Varieties: 1958 (Lecture Notes in Mathematics, 1958) - Softcover

Olsson, Martin C.

Softcover

ISBN 10: 354070518X ISBN 13: 9783540705185

Publisher: Springer, 2008

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2008
• Language: English
• ISBN 10: 354070518X
• ISBN 13: 9783540705185
• Binding: Paperback
• Number of pages: 294