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Science/Engineering Compactifying Moduli Spaces for Abelian Varieties (Lecture Notes in Mathematics)

Posted on 2010-03-16




Name:Science/Engineering Compactifying Moduli Spaces for Abelian Varieties (Lecture Notes in Mathematics)
ASIN/ISBN:354070518X
Language:English
File size:2.3 Mb
ISBN: 354070518X
Publish Date: October 10, 2008
Pages: 286 pages
File Size: 2.30 Mb
Other Info: Springer; djvu (ocr)
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Compactifying Moduli Spaces for Abelian Varieties (Lecture Notes in Mathematics): Martin C. Olsson

This volume presents the construction of canonical modular compactifications ofmoduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides adifferent 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.

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