The Moduli Space of Real Abelian Varieties with Level Structure

Mark Goresky, Yung Sheng Tai
2003 Compositio Mathematica  
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.
doi:10.1023/b:comp.0000005079.56232.e3 fatcat:oin6awwzv5dplnwvoreemybwly