Shimura curves embedded in Igusa's threefold
Abstract
Let O be a maximal order in a totally indefinite quaternion algebra over a totally real number field. In this note we study the locus QO of quaternionic multiplication by O in the moduli space Ag of principally polarized abelian varieties of even dimension g with particular emphasis in the two-dimensional case. We describe QO as a union of Atkin-Lehner quotients of Shimura varieties and we compute the number of irreducible components of QO in terms of class numbers of CM-fields.
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