On the moduli space of diffeomorphic algebraic surfaces

摘要

In this paper we show that the number of deformation types of complex structures on a fixed smooth oriented four-manifold can be arbitrarily large. The examples that we consider in this paper are locally simple abelian covers of rational surfaces. The proof involves the algebraic description of rational blowdowns, classical Brill-Noether theory and deformation theory of normal flat abelian covers.