Moduli Spaces of Abelian Surfaces

Abstract

Let c $\supset {C_F}$ be a fractional ${C_F}$ -ideal. In this chapter we define c-polarized RM abelian surfaces and c-polarized CM abelian surfaces. The moduli space of all c-polarized RM abelian surfaces is a classical Hilbert modular surface, and the moduli space of all c-polarized CM abelian surfaces determines a codimension two cycle on the Hilbert modular surface. Useful references for Hilbert modular surfaces include [10], [14], [19], [46], [54], and [56].