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Birational Geometry of Algebraic Varieties

$67.99 (C)

Part of Cambridge Tracts in Mathematics

  • Date Published: February 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521060226

$ 67.99 (C)

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About the Authors
  • One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.

    • Unique treatment
    • Suitable for non-experts
    • Author is Field's medalist (mathematical equivalent of the Nobel Prize)
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    Reviews & endorsements

    "The book under review, written by two of the leaders in the field, is a comprehensive treatment of the minimal model program...invaluable for the more advanced student of the minimal model program, as well as researchers in the field." Mathematical Reviews

    "...this book, written by two of the main players in this development, answers a demand for a long awaited introductory textbook for the beginners in this field. The expositon is sufficiently elementary, self-contained and comprehensive, and requires fewer prerequisites, so this book will become a standard reference." Bulletin of the American Mathematical Society

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    Product details

    • Date Published: February 2008
    • format: Paperback
    • isbn: 9780521060226
    • length: 264 pages
    • dimensions: 228 x 152 x 17 mm
    • weight: 0.429kg
    • availability: Available
  • Table of Contents

    1. Rational curves and the canonical class
    2. Introduction to minimal model program
    3. Cone theorems
    4. Surface singularities
    5. Singularities of the minimal model program
    6. Three dimensional flops
    7. Semi-stable minimal models.

  • Authors

    Janos Kollár, University of Utah

    Shigefumi Mori, RIMS, Kyoto University, Japan

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