论文标题
使用Kirwan的Desingularization的纯捆的交点共同体
Intersection cohomology of pure sheaf spaces using Kirwan's desingularization
论文作者
论文摘要
Let $\mathbf{M}_n$ be the Simpson compactification of twisted ideal sheaves $\mathcal{I}_{L,Q}(1)$ where $Q$ is a rank $4$ quardric hypersurface in $\mathbb{P}^n$ and $L$ is a linear subspace of dimension $n-2$.本文使用Kirwan的Desingularization方法来计算$ \ Mathbf {M} _n $的庞加莱多项式。我们通过考虑稳定的对和复合物的墙壁交叉，获得了模量$ \ geq 8 $的一维束带的模量带的庞加莱多项式。
Let $\mathbf{M}_n$ be the Simpson compactification of twisted ideal sheaves $\mathcal{I}_{L,Q}(1)$ where $Q$ is a rank $4$ quardric hypersurface in $\mathbb{P}^n$ and $L$ is a linear subspace of dimension $n-2$. This paper calculates the intersection Poincaré polynomial of $\mathbf{M}_n$ using Kirwan's desingularization method. We obtain the intersection Poincaré polynomial of the moduli space for one-dimensional sheaves on del Pezzo surfaces of degree $\geq 8$ by considering wall-crossings of stable pairs and complexes.
