國立清華大學 數學系

Let Q_D be the set of points in Siegel’s modular threefold whose corresponding abelian surfaces have quaternionic multiplication by a maximal order in an indefinite quaternion algebra of discriminant D over the field of rational numbers. In this talk, we first give a formula for the number of irreducible components in Q_D, strengthening an earlier result of Rotger. Then for each irreducible component of genus 0, we describe how to determine its rational parameterization in terms of a Hauptmodul of the associated Shimura curve.