Invariants of Moduli Spaces and Modular Forms

Abstract

Generating functions for invariants of moduli spaces in algebraic geometry of are often related to modular forms. In this paper we give an overview of many instances of this phenomenon and in some cases relate it to predictions from theoretical physics. In this paper we only consider moduli spaces of objects on surfaces. The examples include Euler numbers of moduli spaces of sheaves on surfaces, Donaldson invariants, and enumerative invariants of curves on surfaces.