论文标题
K3表面点的Hilbert方案的全态异常方程
Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
论文作者
论文摘要
我们推测，K3表面上$ n $点的Hilbert方案的Gromov-witten不变性生成系列是Quasi-Jacobi形式，并且满足了一个全体形态异常方程。我们证明了$ 0 $ $ 0 $的猜想，最多只有$ 3 $标记 - 对于所有希尔伯特计划和任意曲线类别。特别是，对于固定的$ n $，所有HyperKähler品种的量子同类均减少了$ k3^{[n]} $ - 类型可以确定为有限的许多系数。 作为一个应用程序，我们表明，$ 2 $ - 点Gromov-Witten类的生成系列是矢量值Jacobi的重量$ -10 $，并且光纤的Donaldson-Thomas-Thomas分区功能是两个Chl Calabi-yau的订单函数，三倍是Jacobi表格。
We conjecture that the generating series of Gromov-Witten invariants of the Hilbert schemes of $n$ points on a K3 surface are quasi-Jacobi forms and satisfy a holomorphic anomaly equation. We prove the conjecture in genus $0$ and for at most $3$ markings - for all Hilbert schemes and for arbitrary curve classes. In particular, for fixed $n$, the reduced quantum cohomologies of all hyperkähler varieties of $K3^{[n]}$-type are determined up to finitely many coefficients. As an application we show that the generating series of $2$-point Gromov-Witten classes are vector-valued Jacobi forms of weight $-10$, and that the fiberwise Donaldson-Thomas partition functions of an order two CHL Calabi-Yau threefold are Jacobi forms.
