Abstract. The moduli space of principally polarized Abelian varieties with real structure and with level N ¼ 4m structure (with m 5 1) is shown to coincide with the set of real points of a quasi-projective algebraic variety defined over Q, and to consist of finitely many copies of the quotient of the space GLðn; RÞ=OðN Þ (of positive definite symmetric matrices) by the principal congruence subgroup of level N in GLðn; ZÞ.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.