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arXiv 2007.062082020-07math.AG

Intersection cohomology of pure sheaf spaces using Kirwan's desingularization

Kiryong Chung, Youngho Yoon

DOI：: 10.1016/j.geomphys.2020.103992

英文摘要：

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 $n-2$. 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.

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