Algebraic Geometry V : Fano Varieties

Fano Varieties

By: V.A. Iskovskikh (Contribution by), Yu.G. Prokhorov (Translator), A.N. Parshin (Editor)

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Hardcover | 1 July 2009

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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.

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Non-Fiction Mathematics Geometry Algebraic Geometry Medicine Medicine in General Probability & Statistics Algebra

Introduction	p. 4
Preliminaries	p. 7
Basic Properties of Fano Varieties	p. 23
Del Pezzo Varieties and Fano Varieties of Large Index	p. 50
Fano Threefolds with [rho]=1	p. 65
Fano Varieties of Coindex 3 with [rho]=1 The Vector Bundle Method	p. 104
Boundedness and Rational Connectedness of Fano Varieties	p. 116
Fano Varieties with [rho][greater than or equal to]2	p. 128
Rationality Questions for Fano Varieties I	p. 153
Rationality Questions for Fano Varieties II	p. 170
Some General Constructions of Rationality and Unirationality	p. 183
Some Particular Results and Open Problems	p. 196
Appendix: Tables	p. 214
References	p. 227
Index	p. 246
Table of Contents provided by Blackwell. All Rights Reserved.

Algebraic Geometry V : Fano Varieties

Fano Varieties

At a Glance

Hardcover

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How to return your order

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