Explicit Birational Geometry of 3-folds (London Mathematical Society Lecture Note Series, Series Number 281)

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.