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

Type 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 program14E05, 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

Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie | CMI Salle 1 | 14 KOL (Browse shelf(Opens below)) | Available | 12015-01 |

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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