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...
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...
Arising from a summer school course taught by Janos Kollar, this book develops the modern theory of rational varieties at a level appropriate for graduate study. Kollar's original course has been developed, with his co-authors, into a state-of-the-art treatment of the classification of algebraic varieties. The authors have included numerous exercises with solutions, which help students reach the stage where they can begin to tackle related contemporary research problems.
Arising from a summer school course taught by Janos Kollar, this book develops the modern theory of rational varieties at a level appropriate for grad...
