Explicit Birational Geometry of 3-folds [Paperback]

This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry.One of the main achievements of algebraic geometry over the last 20 years is the work of Mori and others extending minimal models and the Enriques-Kodaira classification to 3-folds. This book is an integrated suite of papers centred around applications of Mori theory to birational geometry and its 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.One of the main achievements of algebraic geometry over the last 20 years is the work of Mori and others extending minimal models and the Enriques-Kodaira classification to 3-folds. This book is an integrated suite of papers centred around applications of Mori theory to birational geometry and its 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.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.Foreword; 1. One parameter families containing three dimensional torilcä