Explicit birational geometry of 3-folds


Explicit birational geometry of 3-folds

edited by Alessio Corti, Miles Reid

(London Mathematical Society lecture note series, 281)

Cambridge University Press, 2000

  • : pbk

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Includes bibliographical references and index



One of the main achievements of algebraic geometry over the last 30 years is the work of Mori and others extending minimal models and the Enriques-Kodaira classification to 3-folds. This book, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry. Four of the papers (those by Pukhlikov, Fletcher, Corti, and the long joint paper Corti, Pukhlikov and Reid) work out in detail the theory of birational rigidity of Fano 3-folds; these contributions work for the first time with a representative class of Fano varieties, 3-fold hypersurfaces in weighted projective space, and include an attractive introductory treatment and a wealth of detailed computation of special cases.


  • Foreword
  • 1. One parameter families containing three dimensional toric Gorenstein singularities K. Altmann
  • 2. Nonrational covers of CPm x CPn J. Kollar
  • 3. Essentials of the method of maximal singularities A. V. Pukhlikov
  • 4. Working with weighted complete intersections A. R. Iano-Fletcher
  • 5. Fano 3-fold hypersurfaces A. Corti, A. V. Pukhlikov and M. Reid
  • 6. Singularities of linear systems and 3-fold birational geometry A. Corti
  • 7. Twenty five years of 3-folds - an old person's view M. Reid.

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