ENGLISH

Algebraic geometry V. Fano varieties

By A.N. Parshin , I.R. Shafarevich , Yu.G. Prokhorov , S. Tregub , V.A. Iskovskikh

Book information

Publisher
Springer
Year
2001
ISBN
9783540614685, 3540614680
Language
english
Format
DJVU
Filesize
3 MB (3652687 bytes)
Series
Encyclopaedia of Mathematical Sciences 47
Edition
1
Pages
249\249
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

Description

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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