Explicit Birational Geometry of 3-Folds

ISBN-13: 9780521636414 / Angielski / Miękka / 2000 / 356 str.

Alessio Corti; Miles Reid; N. J. Hitchin

Opis

One of the main achievements of algebraic geometry over the past twenty years is the work of Mori and others extending minimal models and the Enriques-Kodaira classification to 3-folds. This integrated suite of papers centers around applications of Mori theory to birational geometry. Four of the papers (those by Pukhlikov, Fletcher, Corti, and the long joint paper by 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 they include an attractive introductory treatment with a wealth of detailed computation of special cases.

Spis treści

Foreword; 1. One parameter families containing three dimensional toric Gorenstein singularities K. Altmann; 2. Nonrational covers of CPm × CPn J. Kollár; 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.