A structure theorem for the gromov-witten invariants of kähler surfaces

Abstract

We prove a structure theorem for the Gromov-Witten invariants of compact Kähler surfaces with geometric genus pg > 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. © 2007 Applied Probability Trust.