The family of lines on the Fano threefold V 5
The family of lines on the Fano threefold V 5
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Fano Threefold V 5 的系列产品
DOI：
10.1017/s0027763000001719
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发表时间：
1989
影响因子：
0.8
通讯作者：
N. Nakayama
中科院分区：
文献类型：
--
作者：
M. Furushima;N. Nakayama
域C上的光滑射影代数3-重V称为Fano 3-重V，如果反正则因子- Kv是充足的。整数g = g（V）= 1/2（- Kv）3称为Fano 3重V的亏格。使得对于某个（样本）可逆层Pic V，λ（- Kv）λ r的最大整数r ∈ 1称为Fano 3重V的指数。设V是指数r = 2的Fano 3重，亏格g = 21，其第二个Betti数b2（V）= 1。则V可以通过线性系统以5次嵌入到P6中，|ℋ|，其中，（- Kv）≠ 2（见Iskovskih [5]）。我们用V5表示这个Fano 3重V。
A smooth projective algebraic 3-fold V over the field C is called a Fano 3-fold if the anticanonical divisor — Kv is ample. The integer g = g(V) = ½(- Kv) 3 is called the genus of the Fano 3-fold V. The maximal integer r ≧ 1 such that ϑ(— Kv)≃ ℋ r for some (ample) invertible sheaf ℋ ε Pic V is called the index of the Fano 3-fold V. Let V be a Fano 3-fold of the index r = 2 and the genus g = 21 which has the second Betti number b2(V) = 1. Then V can be embedded in P6 with degree 5, by the linear system |ℋ|, where ϑ(— Kv)≃ ℋ2 (see Iskovskih [5]). We denote this Fano 3-fold V by V5 .