论文标题
在\ mathbb {p}^2上排名两个向量捆绑包的Segre不变性
On the Segre Invariant for rank two vector bundles on \mathbb{P}^2
论文作者
论文摘要
我们将Segre不变性的概念扩展到表面$ x $上的矢量捆绑包。对于$ x = \ mathbb {p}^2 $，我们确定哪些数字可以作为排名$ 2 $ vector Bundle的segre不变，并带有给定Chern的类别。证明了具有固定Segre不变性的地层的不可约性，并计算了其尺寸。最后，我们向Brill-Noether的理论提出了申请，排名$ 2 $ vector捆绑包$ \ Mathbb {p}^2。$
We extend the concept of Segre's Invariant to vector bundles on a surface $X$. For $X=\mathbb{P}^2$ we determine what numbers can appear as the Segre Invariant of a rank $2$ vector bundle with given Chern's classes. The irreducibility of strata with fixed Segre's invariant is proved and its dimensions are computed. Finally, we present applications to the Brill-Noether's Theory for rank $2$ vector bundles on $\mathbb{P}^2.$
