A Structure Theorem for the Gromov-Witten Invariants of Kahler Surfaces

TL;DR

This paper establishes a structure theorem for Gromov-Witten invariants of certain Kahler surfaces, showing they are governed by universal functions related to the surface's canonical divisor and Euler characteristic.

Contribution

It introduces a new structure theorem for Gromov-Witten invariants of Kahler surfaces with positive geometric genus, under specific geometric conditions.

Findings

Gromov-Witten invariants are determined by universal functions.

Explicit computations of these universal functions in special cases.

The theorem applies to surfaces with a disjoint union of smooth canonical divisor components.

Abstract

We prove a structure theorem for the Gromov-Witten invariants of compact Kahler surfaces with geometric genus $p_g>0$. Under the technical assumption that there is a canonical divisor that is a disjoint union of smooth components, the theorem shows that the GW invariants are universal functions determined by the genus of this canonical divisor components and the holomorphic Euler characteristic of the surface. We compute special cases of these universal functions.