Family Gromov-Witten Invariants for Kahler Surfaces

Abstract

The usual Gromov-Witten invariants are zero for Kähler surfaces with $p_g\ge 1$. In this paper we use analytic methods to define Family Gromov-Witten Invariants for Kähler surfaces. We prove that these are well-defined invariants of the deformation class of the Kähler structure.