The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled 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 re-typeset, 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 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.
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.
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.