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Rational and Nearly Rational Varieties

Rational and Nearly Rational Varieties

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: April 2004
  • availability: Available
  • format: Hardback
  • isbn: 9780521832076


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About the Authors
  • The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.

    • Over one hundred exercises with fully worked out solutions
    • First elementary treatment of rationality questions
    • Mixture of classical and modern methods
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    Reviews & endorsements

    '… a beautiful and ample introduction to the interesting topic of rational and 'nearly rational' varieties and it will be a valuable reference for a wide audience.' Zentralblatt MATH

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    Product details

    • Date Published: April 2004
    • format: Hardback
    • isbn: 9780521832076
    • length: 242 pages
    • dimensions: 236 x 156 x 19 mm
    • weight: 0.58kg
    • availability: Available
  • Table of Contents

    1. Examples of rational varieties
    2. Cubic surfaces
    3. Rational surfaces
    4. Nonrationality and reduction modulo p
    5. The Noether-Fano method
    6. Singularities of pairs
    7. Solutions to exercises.

  • Authors

    János Kollár, Princeton University, New Jersey

    Karen E. Smith, University of Michigan, Ann Arbor

    Alessio Corti, University of Cambridge

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