Algebraic geometry V: fano varieties
Algebraic geometry V: fano varieties
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代数几何 V：fano 簇
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
A. N. Parshin
中科院分区：
文献类型：
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作者：
I. Shafarevich;A. N. Parshin
这项调查的目的由 V.A.伊斯科夫斯基和 Yu.G. Prokhorov 的目的是对 Fano 簇的结构理论进行阐述，即具有充足反规范除数的代数簇。这样的品种自然出现在负小平维品种的双有理分类中，并且非常接近有理品种。这本 EMS 卷涵盖了 Fano 簇分类的不同方法，例如经典的 Fano-Iskovskikh“双投影”方法及其修改、S. Mukai 的矢量丛方法以及极值射线方法。作者讨论了法诺簇的无规则性和理性关联性以及理性问题的最新进展。附录包含法诺品种某些类别的表格。
本书对于代数几何领域的研究人员和研究生来说是非常有用的参考和研究指南。
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.