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Compactifying Moduli Spaces for Abelian Varieties

2008-08-25 Mathematics
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Release : 2008-08-25
Genre : Mathematics
Kind : eBook
Book Rating : 18X/5 ( reviews)

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Book Synopsis Compactifying Moduli Spaces for Abelian Varieties by : Martin C. Olsson

Download or read book Compactifying Moduli Spaces for Abelian Varieties written by Martin C. Olsson. This book was released on 2008-08-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Moduli Spaces of Abelian Surfaces

2011-05-03 Mathematics
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Release : 2011-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 921/5 ( reviews)

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Book Synopsis Moduli Spaces of Abelian Surfaces by : Klaus Hulek

Download or read book Moduli Spaces of Abelian Surfaces written by Klaus Hulek. This book was released on 2011-05-03. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Compactification of Siegel Moduli Schemes

1985-12-12 Mathematics
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Release : 1985-12-12
Genre : Mathematics
Kind : eBook
Book Rating : 530/5 ( reviews)

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Book Synopsis Compactification of Siegel Moduli Schemes by : Ching-Li Chai

Download or read book Compactification of Siegel Moduli Schemes written by Ching-Li Chai. This book was released on 1985-12-12. Available in PDF, EPUB and Kindle. Book excerpt: The main result of this monograph is to prove the existence of the toroidal compactification over Z(1/2).

Compactifying Moduli Spaces

2016-02-04 Mathematics
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Release : 2016-02-04
Genre : Mathematics
Kind : eBook
Book Rating : 212/5 ( reviews)

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Book Synopsis Compactifying Moduli Spaces by : Paul Hacking

Download or read book Compactifying Moduli Spaces written by Paul Hacking. This book was released on 2016-02-04. Available in PDF, EPUB and Kindle. Book excerpt: This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps. Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.

Moduli of Curves and Abelian Varieties

1999-06-29 Gardening
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Release : 1999-06-29
Genre : Gardening
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Book Synopsis Moduli of Curves and Abelian Varieties by : Carel Faber

Download or read book Moduli of Curves and Abelian Varieties written by Carel Faber. This book was released on 1999-06-29. Available in PDF, EPUB and Kindle. Book excerpt: The Dutch Intercity Seminar on Moduli, which dates back to the early eighties, was an initiative of G. van der Geer, F. Oort and C. Peters. Through the years it became a focal point of Dutch mathematics and it gained some fame, also outside Holland, as an active biweekly research seminar. The tradition continues up to today. The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Hain, E. Looijenga, and F. Oort, originates from the seminar held in 1995--96. Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles. Topics include a stratification of a moduli space of abelian varieties in positive characteristic, and the calculation of the classes of the strata, tautological classes for moduli of abelian varieties as well as for moduli of curves, correspondences between moduli spaces of curves, locally symmetric families of curves and jacobians, and the role of symmetric product spaces in quantum field theory, string theory and matrix theory.

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