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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.

Threefolds (Algebraic geometry) --- Geometry, Algebraic. --- Surfaces, Algebraic. --- Algebraic surfaces --- Geometry, Algebraic --- Algebraic geometry --- Geometry --- 3-folds (Algebraic geometry) --- Three-folds (Algebraic geometry) --- Algebraic varieties

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Group theory --- Algebraic geometry --- 3-folds (Algebraic geometry) --- Coefficiententheorie --- Drievouden (Algebraïsche geometrie) --- Moduli theory --- Oppervlakken [Algebraïsche ] --- Surfaces [Algebraic ] --- Surfaces algébriques --- Theorie des coefficients --- Three-folds (Algebraic geometry) --- Threefolds (Algebraic geometry) --- Variétés à 3 dimensions --- Moduli theory. --- Surfaces, Algebraic. --- Threefolds(Algebraic geometry) --- Surfaces, algebraic

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51 <082.1> --- Mathematics--Series --- Moduli theory. --- Surfaces, Cubic --- Threefolds (Algebraic geometry) --- Variétés topologiques à 4 dimensions --- Surfaces cubiques --- Variétés à 3 dimensions --- Surfaces, Cubic. --- Variétés topologiques à 4 dimensions --- Variétés à 3 dimensions --- Algebraic geometry --- Moduli theory --- 3-folds (Algebraic geometry) --- Three-folds (Algebraic geometry) --- Algebraic varieties --- Geometry, Algebraic --- Cubic surfaces --- Theory of moduli --- Analytic spaces --- Functions of several complex variables --- Modules, Théorie des --- Géométrie algébrique --- Hodge theory. --- Hodge, Théorie de. --- Fonctions de plusieurs variables complexes