2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62020The moduli space of principally polarized abelian varieties with real structure and with level $N=4m$ structure (with $m \ge 1$) is shown to coincide with the set of real points of a quasi-projective algebraic variety defined over $\mathbb Q$, and to consist of finitely many copies of the quotient of the space $\mathbf{GL}(n, \mathbb R)/\mathbf O(N)$ (of positive definite symmetric matrices) by the principal congruence subgroup of level $N$ in $\mathbf{GL}(n, \mathbb Z).$Algebraic GeometryRepresentation Theory11G15; 14P05text