Universal Series for Hilbert Schemes and Strange Duality
Universal Series for Hilbert Schemes and Strange Duality
复制标题
希尔伯特方案和奇异对偶的通用级数
DOI：
10.1093/imrn/rny101
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Drew Johnson
中科院分区：
文献类型：
--
作者：
Drew Johnson
我们展示了如何“有限报价计划方法”适用于Le Potier的奇怪的对偶德尔Pezzo表面导致aptures（适用于所有光滑的复杂的射影表面）有关的两套普遍的权力系列的希尔伯特计划的点的表面：那些顶部陈类重言式层，和那些欧拉特性的线束。我们已经验证了这些预测计算低阶。然后，我们给出了一个小的行列中的分析。我们还给出了一个公式的组合证明：$S^{[n]}$上重言式层与一个点的结构层相关联的顶Chern类等于$（-1）^n$乘以$n$th Catalan数。
We show how the "finite Quot scheme method" applied to Le Potier's strange duality on del Pezzo surfaces leads to conjectures (valid for all smooth complex projective surfaces) relating two sets of universal power series on Hilbert schemes of points on surfaces: those for top chern classes of tautological sheaves, and those for Euler characteristics of line bundles. We have verified these predictions computationally for low order. We then give an analysis of these conjectures in small ranks. We also give a combinatorial proof of a formula predicted by our conjectures: the top chern class of the tautological sheaf on $S^{[n]}$ associated to the structure sheaf of a point is equal to $(-1)^n$ times the $n$th Catalan number.