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Compactifying Moduli Spaces for Abelian Varieties
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Compactifying Moduli Spaces for Abelian Varieties Paperback - 2008 - 2008th Edition

by Martin C. Olsson

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From the publisher

The problem of compactifying the moduli spaceA of principally polarized g abelian varieties has a long and rich history. The majority of recent work has focusedonthe toroidal compacti?cations constructed over C by Mumford and his coworkers, and over Z by Chai and Faltings. The main drawback of these compacti?cations is that they are not canonical and do not represent any r- sonable moduli problem on the category of schemes. The starting point for this work is the realization of Alexeev and Nakamura that there is a canonical compacti?cation of the moduli space of principally polarized abelian varieties. Indeed Alexeev describes a moduli problem representable by a proper al- braic stack over Z which containsA as a dense open subset of one of its g irreducible components. In this text we explain how, using logarithmic structures in the sense of Fontaine, Illusie, and Kato, one can de?ne a moduli problem "carving out" the main component in Alexeev's space. We also explain how to generalize the theory to higher degree polarizations and discuss various applications to moduli spaces for abelian varieties with level structure.

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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.

Details

  • Title Compactifying Moduli Spaces for Abelian Varieties
  • Author Martin C. Olsson
  • Binding Paperback
  • Edition number 2008th
  • Edition 2008
  • Pages 286
  • Volumes 1
  • Language ENG
  • Publisher Springer
  • Publication date 2008-08-25
  • Features Bibliography, Index, Table of Contents
  • ISBN 9783540705185 / 354070518X
  • Weight 1 lbs (0.45 kg)
  • Dimensions 9.2 x 6.1 x 0.7 in (23.37 x 15.49 x 1.78 cm)
  • Category Mathematics
  • Library of Congress Catalogue Number 2008931163
  • Dewey Decimal Code 516.353

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Compactifying Moduli Spaces for Abelian Varieties
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Compactifying Moduli Spaces for Abelian Varieties

by Olsson, Martin C.

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Springer, 2008. This is an ex-library book and may have the usual library/used-book markings inside.This book has soft covers. In good all round condition. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,550grams, ISBN:9783540705185
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Compactifying Moduli Spaces for Abelian Varieties

Compactifying Moduli Spaces for Abelian Varieties

by Martin C. Olsson

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Paperback. New. New Book; Fast Shipping from UK; Not signed; Not First Edition; 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.
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Compactifying Moduli Spaces For Abelian Varieties
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Compactifying Moduli Spaces For Abelian Varieties

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

by Martin C. Olsson

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Springer Verlag, 2008. Paperback. New. 1st edition. 286 pages. 9.00x6.00x0.75 inches.
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Compactifying Moduli Spaces For Abelian Varieties
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Compactifying Moduli Spaces For Abelian Varieties

by Olsson, Martin C,

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Compactifying Moduli Spaces for Abelian Varieties (Lecture Notes in Mathematics, 1958)
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Compactifying Moduli Spaces for Abelian Varieties (Lecture Notes in Mathematics, 1958)

by Olsson, Martin C.

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paperback. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book.
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