Titlebook: Compactifying Moduli Spaces for Abelian Varieties; Martin C. Olsson Book 2008 Springer-Verlag Berlin Heidelberg 2008 Abelian varieties.Abe

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Liability

Reimund Anhut,Wilhelm HeitmeyerIn this chapter we discuss the logarithmic interpretation of the main component of the moduli spaces for “broken toric varieties” considered by Alexeev. This study contains many of the basic ideas used later for our study of abelian varieties. The reader only interested in abelian varieties can, however, skip directly to chapter 4.

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Preliminaries,In this chapter we review some background material used in the main part of the text. The experienced reader may wish to just skim this chapter for our notational conventions and then proceed to chapter 3.

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Moduli of Broken Toric Varieties,In this chapter we discuss the logarithmic interpretation of the main component of the moduli spaces for “broken toric varieties” considered by Alexeev. This study contains many of the basic ideas used later for our study of abelian varieties. The reader only interested in abelian varieties can, however, skip directly to chapter 4.

不能妥协

Book 2008n 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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Book 2008ructure), 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 introductio

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使显得不重要

Moduli of Abelian Varieties with Higher Degree Polarizations,lly on . there exists an ample line bundle . on . such that the map . is equal to λ. In this case if . : . → . is the structural morphism then . is locally free of rank . on . and its formation commutes with arbitrary base change on . (see for example [36, I, §1] for a summary of basic properties of ample line bundles on abelian varieties).