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Algebraic Geometry V: Fano Varieties
Paperback
Series: Encyclopaedia of Mathematical Sciences, Book 47
Medical ReferenceGeometryProbability & Statistics
ISBN13: 9783642082603
Publisher: Springer
Published: Dec 1 2010
Pages: 247
Weight: 0.80
Height: 0.54 Width: 6.14 Depth: 9.21
Language: English
The aim of this survey, written by V.A. Iskovskikh and Yu.G. Prokhorov, 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.
This book will be very useful as a reference and research guide for researchers and graduate students in algebraic geometry.
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