2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62016For appropriate $N\ge 3$ and $d<0,$ the moduli space of principally polarized abelian surfaces with level $N$ structure and anti-holomorphic multiplication by $\mathcal O_d$ (the ring of integers in $\mathbb Q(\sqrt{d})$) is shown to consist of the real points of a quasi-projective algebraic variety defined over $\mathbb Q$, and to coincide with finitely many copies of the quotient of hyperbolic 3-space by the principal congruence subgroup of level $N$ in $\mathbf{SL}(2, \mathcal O_d).$Algebraic GeometryRepresentation Theory11G15 14P05text