TY  - BOOK
AU  - Parshin,,A.N.
AU  - Shafarevich,,I.R.
AU  - Prokhorov,,YuG.
AU  - Prokhorov,,YuG.
AU  - Tregub,,S.
AU  - Iskovskikh,,V.A.
TI  - Algebraic geometry V: fano varieties
SN  - 3540614680
U1  - 516 
PY  - 2001///
CY  - [S.l.]
PB  - Springer
KW  - Algebra
KW  - Algebraic Geometry
KW  - Mathematics
KW  - Medical / Nursing
KW  - Science/Mathematics
KW  - General
KW  - Geometry - Algebraic
KW  - Mathematics / Geometry / Algebraic
KW  - Mathematics / Probability & Statistics / General
KW  - Medical / General
KW  - Probability & Statistics - General
N1  - 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
ER  -