论文标题
关于一般完整交叉点线性空间的FANO方案
On Fano schemes of linear spaces of general complete intersections
论文作者
论文摘要
我们考虑$ k $的fano方案$ f_k（x）$ - 多维$ x \ subset \ subset \ mathbb {p}^n $多维$ \ usepline {d d_1，d_1，\ ldots，d_s）$的多维线性子空间。我们的主要结果是Riedl和Yang的结果的扩展是在非常普遍的高度曲面上涉及的线条方案：我们考虑$ x $是非常一般的完整交叉点，而$π_{i = 1}^s d_i> 2 $的情况下曲线。在论文的最后，我们研究了$π_{i = 1}^s d_i = 2 $。
We consider the Fano scheme $F_k(X)$ of $k$--dimensional linear subspaces contained in a complete intersection $X \subset \mathbb{P}^n$ of multi--degree $\underline{d} = (d_1, \ldots, d_s)$. Our main result is an extension of a result of Riedl and Yang concerning Fano schemes of lines on very general hypersurfaces: we consider the case when $X$ is a very general complete intersection and $Π_{i=1}^s d_i > 2$ and we find conditions on $n$, $\underline{d}$ and $k$ under which $F_k(X)$ does not contain either rational or elliptic curves. At the end of the paper, we study the case $Π_{i=1}^s d_i = 2$.
