Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
G Oberdieck - Geometry & Topology, 2024 - msp.org
Geometry & Topology, 2024•msp.org
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 three 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.
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 three 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.
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 three 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.
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