Smooth Compactifications of Locally Symmetric Varieties / Edition 2

Smooth Compactifications of Locally Symmetric Varieties / Edition 2

by Avner Ash, David Mumford, Michael Rapoport, Yung-sheng Tai
     
 

ISBN-10: 0521739551

ISBN-13: 9780521739559

Pub. Date: 02/28/2010

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521739559
Publisher:
Cambridge University Press
Publication date:
02/28/2010
Series:
Cambridge Mathematical Library Series
Edition description:
Second Edition
Pages:
240
Product dimensions:
5.90(w) x 8.90(h) x 0.60(d)

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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