Birational geometry of algebraic varieties / Janos Kollar, Shigefumi Mori ; C. H. Clemens, A. Corti

Auteur principal : Kollár, János, 1956-, AuteurCo-auteur : Mori, Shigefumi, 1951-, AuteurAuteur secondaire : Clemens, Charles Herbert, 1939-, Collaborateur • Corti, Alessio, 1965-, CollaborateurType de document : MonographieCollection : Cambridge tracts in mathematics, 134Langue : anglais.Pays: Grande Bretagne.Éditeur : Cambridge : Cambridge University Press, 1998Description : 1 vol. (VIII-254 p.) ; 24 cmISBN: 0521632773.ISSN: 0950-6284.Bibliographie : Bibliogr. p. 241-247. Index.Sujet MSC : 14E30, Algebraic geometry - Birational geometry, Minimal model program
14E05, Algebraic geometry - Birational geometry, Rational and birational maps
14J30, Algebraic geometry - Surfaces and higher-dimensional varieties, 3-folds
14C35, Algebraic geometry - Cycles and subschemes, Applications of methods of algebraic K-theory
14J40, Algebraic geometry - Surfaces and higher-dimensional varieties, n-folds (n>4)
En-ligne : Zentralblatt | MathSciNet
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Chapter 1 is an introduction to the minimal model program, and the results proved here provide the conceptual foundation for the whole book. Chapter 2 discusses the role of certain classes of singularities and some generalizations of the Kodaira vanishing theorem. In chapter 3 the cone theorem (valid in all dimensions) is proved. This is the first important ingredient of the theory. The last three chapters deal with the 3-dimensional flips and flops. These are essentially new birational transformations in order to reach the minimal model. A special attention is devoted to some special classes of surface singularities or to the singularities occurring in the minimal model program in dimension 3. Chapter 6 is devoted to flops (which are easier to be understood than flips), and the last chapter to 3-dimensional flips. The theory of 3-dimensional flips is technically the most complicated part, and precisely here the authors manage to simplify considerably many proofs. (Zentralblatt)

Bibliogr. p. 241-247. Index

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