Smooth Compactifications of Locally Symmetric Varieties / Edition 2

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The new edition of this celebrated and long-unavailable book preserves much of the content and structure of the original, which is still unrivaled in its presentation of a universal method for the resolution of a class of singularities in algebraic geometry. At the same time, the book has been completely retypeset, errors have been eliminated, proofs have been streamlined, the notation has been made consistent and uniform, an index has been added, and a guide to recent literature has been added. The authors begin by reviewing key results in the theory of toroidal embeddings and by explaining examples that illustrate the theory. Chapter II develops the theory of open self-adjoint homogeneous cones and their polyhedral reduction theory. Chapter III is devoted to basic facts on hermitian symmetric domains and culminates in the construction of toroidal compactifications of their quotients by an arithmetic group. The final chapter considers several applications of the general results. The book brings together ideas from algebraic geometry, differential geometry, representation theory and number theory, and will continue to prove of value for researchers and graduate students in these areas.
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Editorial Reviews

From the Publisher
'The book under review is a new edition of the authors' celebrated research monograph … which must be seen as one of the milestones in contemporary algebraic and complex-analytic geometry … No doubt, this classic will maintain its outstanding role in algebraic geometry, Hermitian differential geometry, group representation theory, and arithmetic geometry also in the future, especially for active researchers and graduate students in these related areas of contemporary pure mathematics. In this regard, the present new edition of it is certainly more than welcome.' Zentralblatt MATH
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Product Details

  • ISBN-13: 9780521739559
  • Publisher: Cambridge University Press
  • Publication date: 2/28/2010
  • Series: Cambridge Mathematical Library Series
  • Edition description: Second Edition
  • Edition number: 2
  • Pages: 240
  • Product dimensions: 5.90 (w) x 8.90 (h) x 0.60 (d)

Meet the Author

Avner Ash is Professor in the Department of Mathematics at Boston College, Massachusetts.

David Mumford is Professor Emeritus of Applied Mathematics at Brown University, Rhode Island.

Michael Rapoport is Professor in the Mathematical Institute of the University of Bonn, Germany.

Yung-sheng Tai is Associate Professor of Mathematics at Haverford College, Pennsylvania.

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Table of Contents

Preface to the second edition; Preface to the first edition; 1. Basics on torus embeddings: examples; 2. Polyhedral reduction theory in self-adjoint cones; 3. Compactifications of locally symmetric varieties; 4. Further developments; Supplementary bibliography; Index.
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