Year: 2024
Type: article
Abstract: 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.
Source: Geometry & Topology
Author: Georg Oberdieck
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4221150874