Explicit birational geometry of 3-folds / edited by Alessio Corti, Miles Reid.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Alessio Corti and Miles Reid -- Foreword / Klaus Altmann -- One parameter families contaning three dimensional toric gorenstein singularities / János Kollár -- Nonrational covers of CPm X CPn / Aleksandr V. Pukhlikov -- Essentials of the method of maximal singularities / A.R. Iano-Fletcher -- Working with weighted complete intersections / Alessio Corti, Aleksandr Pukhlikov and Miles Reid -- Fano 3-fold hypersurfaces / Alessio Cortio -- Singularities of linear systems and 3-fold birational geometry / Miles Reid -- Twenty five years of 3-folds-an old person's view.

One of the main achievements of algebraic geometry over the last 30 years is the work of Mori and others extending minimal models and the Enriques-Kodaira classification to 3-folds. This book, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry. Four of the papers (those by Pukhlikov, Fletcher, Corti, and the long joint paper 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 include an attractive introductory treatment and a wealth of detailed computation of special cases.