论文标题
Del Pezzo三倍的Ulrich捆绑包
Ulrich bundles on Del Pezzo threefolds
论文作者
论文摘要
我们证明，对于任何$ r \ geq 2 $，稳定的ulrich ulrich捆绑套件的模量空间和确定性$ \ nathcal o_x（r）$上的任何平滑的fano fano fano三倍的索引二的索引二是dimension $ r^2+1 $的平滑，即使在$ r $中都不是$ r $的，也不是零件。特别是这表明任何这样的三倍都是Ulrich Wild。作为初步结果，我们为在三倍的曲线中存在三倍的特殊特性而在任何平滑的投影三倍上都存在乌尔里希捆绑包。
We prove that for any $r \geq 2$ the moduli space of stable Ulrich bundles of rank $r$ and determinant $\mathcal O_X(r)$ on any smooth Fano threefold $X$ of index two is smooth of dimension $r^2+1$ and that the same holds true for even $r$ when the index is four, in which case no odd--rank Ulrich bundles exist. In particular this shows that any such threefold is Ulrich wild. As a preliminary result, we give necessary and sufficient conditions for the existence of Ulrich bundles on any smooth projective threefold in terms of the existence of a curve in the threefold enjoying special properties.
