Explicit Birational Geometry of 3-folds

doi:10.1017/CBO9780511758942

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.

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Explicit Birational Geometry of 3-folds

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Foreword
pp 1-20

One parameter families containing three dimensional toric Gorenstein singularities
pp 21-50

Nonrational covers of ℂℙm × ℂℙn
pp 51-72

Essentials of the method of maximal singularities
pp 73-100

Working with weighted complete intersections
pp 101-174

Fano 3-fold hypersurfaces
pp 175-258

Singularities of linear systems and 3-fold birational geometry
pp 259-312

Twenty five years of 3-folds – an old person's view
pp 313-344

Index
pp 345-349

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