+612 9045 4394
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.
| 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. |
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
