Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8
Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8
复制标题
8 属法诺三重上的普法夫线和矢量丛
DOI：
10.1090/s1056-3911-07-00440-7
复制
发表时间：
2005
影响因子：
1.8
通讯作者：
L. Manivel
中科院分区：
文献类型：
--
作者：
A. Iliev;L. Manivel
令$X$为属8的一般复法诺三重。我们证明$X$上陈数$c_1=1$、$c_2=6$和$c_3=0$的二阶半稳定滑轮的模空间与$X$上二次曲线的Fano曲面$F(X)$同构。该表面是光滑的，并且与与 $X$ 三次方正交的线的 Fano 表面同构。在 $F(X)$ 内部，非局部自由滑轮由与 X 上的线族基同构的 26 平滑曲线参数化。
Let $X$ be a general complex Fano threefold of genus 8. We prove that the moduli space of rank two semistable sheaves on $X$ with Chern numbers $c_1=1$, $c_2=6$ and $c_3=0$ is isomorphic to the Fano surface $F(X)$ of conics on $X$. This surface is smooth and isomorphic to the Fano surface of lines in the orthogonal to $X$ cubic threefold. Inside $F(X)$, the non-locally free sheaves are parameterized by a smooth curve of genus 26 isomorphic to the base of the family of lines on X.