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.
Contributions by:
V.A. Iskovskikh Edited by:
A.N. Parshin, I.R. Shafarevich Translated by:
Yu.G. Prokhorov, S. Tregub Imprint: Springer Verlag Country of Publication: Germany Volume: v.47 Dimensions:
Height: 235mm,
Width: 155mm,
Spine: 15mm
Weight: 1.190kg ISBN:9783540614685 ISBN 10: 3540614680 Series:Encyclopaedia of Mathematical Sciences Pages: 256 Publication Date:27 November 1998 Audience:
College/higher education
,
Professional and scholarly
,
Further / Higher Education
,
Undergraduate
Format:Hardback Publisher's Status: Active
