Non-normal del Pezzo durfaces and Fano threefolds of the first kind.
Non-normal del Pezzo durfaces and Fano threefolds of the first kind.
复制标题
非正态的 del Pezzo durfaces 和 Fano 是第一类的三倍。
DOI：
10.1515/crll.1992.429.183
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
M. Furushima
中科院分区：
文献类型：
--
作者：
M. Tada;M. Furushima
设V是指数为2的第一类Fano三重图，即反正则线B ndle-Kv在F上是充分的，且Pic V ∈ Z（-\KV}.由Shokurov [Sh]可知，线性系统中存在光滑元H|- \KV|，这是一个del Pezzo曲面，也就是说，H可以通过在一般位置的r（^ 8）点处爆破而从P获得（参见图1）。[De])或P * x P.相反，线性系统|- \KV|并不一定包含一个“非正常”成员，我们将在下面看到。在本文中，我们将确定线性系统的“非正规”成员矩阵的结构|- KV
Let V be a Fano threefold of the first kind with index two, namely, the anti-canonical line b ndle -Kv is ample on Fand Pic V ̂ Z(-\KV}. By Shokurov [Sh], one knows that there exists a smooth member H in the linear System | — \KV |, which is a del Pezzo surface, that is, H can be obtained from P by blowing up at r (^ 8) points in general position (cf. [De]) or P * x P. On the contrary, the linear System | — \KV | does not necessarily contain a "non-normal" member Υ s we will see below. Now, in this paper, we will determine the structure of "non-normal" member Υ of the linear System | — \KV\.