Compactifying Moduli Spaces for Abelian Varieties

Martin C. Olsson

ISBN 10: 354070518X / ISBN 13: 9783540705185

Editore: Springer Berlin Heidelberg, 2008

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Druck auf Anfrage Neuware - Printed after ordering - Thisvolume 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.

Codice articolo 9783540705185

Dati bibliografici

• Titolo: Compactifying Moduli Spaces for Abelian Varieties
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 354070518X
• ISBN 13: 9783540705185
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

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.