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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.
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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.
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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)
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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)
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Compactifying Moduli Spaces for Abelian Varieties
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Thisvolume 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. 296 pp. Englisch. Seller Inventory # 9783540705185
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Compactifying Moduli Spaces for Abelian Varieties
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Kartoniert / Broschiert. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Includes supplementary material: sn.pub/extrasA 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. Seller Inventory # 4898965
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Compactifying Moduli Spaces for Abelian Varieties (Lecture Notes in Mathematics)
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Compactifying Moduli Spaces for Abelian Varieties
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Taschenbuch. Condition: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 296 pp. Englisch. Seller Inventory # 9783540705185
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Compactifying Moduli Spaces for Abelian Varieties
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Thisvolume 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. Seller Inventory # 9783540705185
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Compactifying Moduli Spaces for Abelian Varieties (Lecture Notes in Mathematics)
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