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

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