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Compactifying Moduli Spaces for Abelian Varieties [electronic resource] / by Martin C. Olsson.

By: Contributor(s): Material type: TextTextSeries: Lecture Notes in MathematicsPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008Description: VIII, 286 p. 1 illus. online resourceContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540705192
Subject(s): Additional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification:
  • 516.35 23
LOC classification:
  • QA564-609
Online resources:
Contents:
A Brief Primer on Algebraic Stacks -- Preliminaries -- Moduli of Broken Toric Varieties -- Moduli of Principally Polarized Abelian Varieties -- Moduli of Abelian Varieties with Higher Degree Polarizations -- Level Structure.
In: Springer eBooksSummary: 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
E-BOOKS ISI Library, Kolkata Not for loan EB1507
Total holds: 0

A Brief Primer on Algebraic Stacks -- Preliminaries -- Moduli of Broken Toric Varieties -- Moduli of Principally Polarized Abelian Varieties -- Moduli of Abelian Varieties with Higher Degree Polarizations -- Level Structure.

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.

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