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08-30-2009, 07:45 PM
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Algebraic Geometry V: Fano Varieties
Springer | 2001-05-02 | ISBN: 3540614680 | Djvu | 247 pages | 3,5 Mb The aim of this survey is to provide an exposition of the structure theory of Fano varieties, i.e. algebraic vareties with an ample anticanonical divisor. Such varieties naturally appear in the birational classification of varieties of negative Kodaira dimension, and they are very close to rational ones. This EMS volume covers different approaches to the classification of Fano varieties such as the classical Fano-Iskovskikh “double projection” method and its modifications, the vector bundles method due to S. Mukai, and the method of extremal rays. The authors discuss uniruledness and rational connectedness as well as recent progress in rationality problems of Fano varieties. The appendix contains tables of some classes of Fano varieties.
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