Classification of Fano 3-folds with B2≥2
Classification of Fano 3-folds with B2≥2
复制标题
B2≥2 的 Fano 3 倍分类
DOI：
10.1007/s00229-002-0336-2
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发表时间：
1981
影响因子：
0.6
通讯作者：
S. Mukai
中科院分区：
文献类型：
--
作者：
S. Mori;S. Mukai
本文给出了B2≥2的Fano 3-折叠的分类。有确切的87种类型的这种3-folds的变形;一个Fano 3-folds同构于一个产品的Pl和一个del Pezzo曲面，如果它的第二贝蒂数不小于6。特别地，Fano 3倍的第二贝蒂数不大于10。首先利用文[2]中发展的工具对原始的或B2=2的Fano 3-folds进行分类，然后利用它们的锥束结构或其上直线的存在性，研究由它们通过连续曲线爆破得到的Fano 3-folds。
This article contains the classification of Fano 3-folds with B2≥2. There exist exactly 87 types of such 3-folds up to deformations; a Fano 3-fold is isomorphic to a product of Pl and a del Pezzo surface if its second Betti number is not less than 6. In particular, the second Betti number of a Fano 3-fold is not greater than 10. Firstly we classify Fano 3-folds which are either primitive or have B2=2 by the tools developed in [2]; then we study Fano 3-folds obtained from them by successive curve-blow-ups by using their conic bundle structures or the existence of lines on them.