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Compactifying Moduli Spaces for Abelian Varieties

Compactifying Moduli Spaces for Abelian Varieties PDF Author: Martin C. Olsson
Publisher: Springer Science & Business Media
ISBN: 354070518X
Category : Mathematics
Languages : en
Pages : 286

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Book Description
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.