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Algebraic Geometry V : Fano Varieties :  Fano Varieties - A.N. Parshin

Algebraic Geometry V : Fano Varieties

Fano Varieties

By: A.N. Parshin (Editor), I. R. Shafarevich (Editor), Y.G. Prokhorov (Translator), S. Tregub (Translator)

Hardcover Published: July 2009
ISBN: 9783540614685
Number Of Pages: 247

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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.

Introductionp. 4
Preliminariesp. 7
Basic Properties of Fano Varietiesp. 23
Del Pezzo Varieties and Fano Varieties of Large Indexp. 50
Fano Threefolds with [rho]=1p. 65
Fano Varieties of Coindex 3 with [rho]=1 The Vector Bundle Methodp. 104
Boundedness and Rational Connectedness of Fano Varietiesp. 116
Fano Varieties with [rho][greater than or equal to]2p. 128
Rationality Questions for Fano Varieties Ip. 153
Rationality Questions for Fano Varieties IIp. 170
Some General Constructions of Rationality and Unirationalityp. 183
Some Particular Results and Open Problemsp. 196
Appendix: Tablesp. 214
Referencesp. 227
Indexp. 246
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540614685
ISBN-10: 3540614680
Series: Encyclopaedia of Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 247
Published: July 2009
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 1.19

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