Algebraic Geometry V: Fano Varieties: 47 (Encyclopaedia of Mathematical Sciences, 47) - Hardcover

Hardcover

ISBN 10: 3540614680 ISBN 13: 9783540614685

Publisher: Springer, 1998

Synopsis

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.

About this title

Product Description

This EMS volume provides an exposition of the structure theory of Fano varieties, i.e. algebraic varieties with an ample anticanonical divisor. This book will be very useful as a reference and research guide for researchers and graduate students in algebraic geometry.

Edition details

• Publisher: Springer
• Publication date: 1998
• Language: English
• ISBN 10: 3540614680
• ISBN 13: 9783540614685
• Binding: Hardcover
• Number of pages: 252
• Editor: Parshin A.N., Shafarevich I.R.