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Birational Geometry of Algebraic Varieties


Part of Cambridge Tracts in Mathematics

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

£ 27.99

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About the Authors
  • One of the major discoveries of the last two decades of the twentieth century 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 a 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

    Review of the hardback: '… the book is very crisply written, unusually easy to read for a book covering advanced material, and is moreover very concise for the book for reference, but is also an ideal book on which to base a series of seminars for research students, or indeed for research students to read by themselves.' P. M. H. Wilson, Bulletin of the London Mathematical Society

    Review of the hardback: '… a very good survey of present research.' European Mathematical Society

    Review of the hardback: 'I can recommend it to anyone wanting to get a deeper knowledge than just getting a survey of some facts on the classification theory.' M. Coppens, Niew Archief voor Wiskunde

    Review of the hardback: '… a very good survey of present research … a very clear presentation of the subject.' EMS

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    Product details

    • Date Published: April 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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