Compactifying Moduli Spaces for Abelian Varieties
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Beschreibung
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.
Includes supplementary material: sn.pub/extras
Autor*in
Martin C. Olsson
Themen in »Compactifying Moduli Spaces for Abelian Varieties«
Abelian varieties Abelian variety Canon Compactification Moduli Prime Volume algebra compactifications construction geometry group logarithm techniques
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From the reviews:
"No doubt, the work presented in this research monograph is a fundamental contribution to the compactification theory of moduli spaces in general, and of moduli spaces for abelian varieties in particular. … the present monograph is written in a very lucid, comprehensive, largely self-contained and enlightening style, including numerous additional remarks and hints." (Werner Kleinert, Zentralblatt MATH, Vol. 1165, 2009)
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