Editors:
- Only reference on Fano manifolds.
Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 47)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
About this book
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.
Bibliographic Information
Book Title: Algebraic Geometry V
Book Subtitle: Fano Varieties
Editors: A.N. Parshin, I.R. Shafarevich
Series Title: Encyclopaedia of Mathematical Sciences
Publisher: Springer Berlin, Heidelberg
Copyright Information: Springer-Verlag Berlin Heidelberg 1999
Hardcover ISBN: 978-3-540-61468-5Published: 27 November 1998
Softcover ISBN: 978-3-642-08260-3Published: 01 December 2010
Series ISSN: 0938-0396
Edition Number: 1
Number of Pages: V, 247
Additional Information: Original Russian edition published by VINITI, Moscow