On Okounkovs Conjecture Connecting Hilbert Schemes of Points and Multiple -Zeta Values
On Okounkovs Conjecture Connecting Hilbert Schemes of Points and Multiple -Zeta Values
复制标题
论连接希尔伯特点格式和多重Zeta值的奥孔科夫猜想
DOI：
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发表时间：
2018
影响因子：
1
通讯作者：
Fei Yu
中科院分区：
文献类型：
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作者：
Zhenbo Qin;Fei Yu
本文计算了光滑射影曲面上点的Hilbert方案的切丛的全Chern类与这些Hilbert方案上重言丛的Chern特征标之间的交对的生成级数。模较低的权重项，我们验证Okounkov的猜想[13]连接这些希尔伯特计划和多个q-zeta值。另外，当曲面是阿贝尔曲面时，也完全证明了这个猜想。我们还确定了关于这些Hilbert格式的切丛的全Chern类的Boissiére和Nieper-Wisskirchen [1，2]意义下的一些普适常数。本文的主要方法是使用Carlsson和Okounkov在Carlsson [5，6]中概述的设置以及Li，Qin和Wang [10]中证明的Chern特征算子的结构。
We compute the generating series for the intersection pairings between the total Chern classes of the tangent bundles of the Hilbert schemes of points on a smooth projective surface and the Chern characters of tautological bundles over these Hilbert schemes. Modulo the lower weight term, we verify Okounkov’s conjecture [13] connecting these Hilbert schemes and multiple q-zeta values. In addition, this conjecture is completely proved when the surface is abelian. We also determine some universal constants in the sense of Boissiére and Nieper-Wisskirchen [1, 2] regarding the total Chern classes of the tangent bundles of these Hilbert schemes. The main approach of this article is to use the set-up of Carlsson and Okounkov outlined in Carlsson [5, 6] and the structure of the Chern character operators proved in Li, Qin, and Wang [10].