论文标题
光滑的投射表面和广义的kummer品种的希尔伯特积分方案具有有限的小组动作
Hilbert schemes of points on smooth projective surfaces and generalized Kummer varieties with finite group actions
论文作者
论文摘要
Göttsche和soergel提供了平滑代数表面上的Hilbert方案的杂物数量和广义Kummer品种的杂物数量的公式。当一个光滑的投射表面$ S $承认有限的$ g $的操作时，我们通过点计数描述了$ g $的动作。 $ g $的每个元素都对$ \ sum_ {n = 0}^{\ infty} \ sum_ {i = 0}^{\ infty}（ - 1）^{i}如果$ s $是K3表面或Abelian表面，则产生的生成功能会在$ g $忠实地和符合$ S $上的作用时提供一些有趣的模块化表格。
Göttsche and Soergel gave formulas for the Hodge numbers of Hilbert schemes of points on a smooth algebraic surface and the Hodge numbers of generalized Kummer varieties. When a smooth projective surface $S$ admits an action by a finite group $G$, we describe the action of $G$ on the Hodge pieces via point counting. Each element of $G$ gives a trace on $\sum_{n=0}^{\infty}\sum_{i=0}^{\infty}(-1)^{i}H^{i}(S^{[n]},\mathbb{C})q^{n}$. In the case that $S$ is a K3 surface or an abelian surface, the resulting generating functions give some interesting modular forms when $G$ acts faithfully and symplectically on $S$.
