Moduli space of real abelian varieties with level structure

2001/08/15 by Mark Goresky, Goresky, Mark, Yung sheng Tai +1
Computer Science · Mathematics · #11G15 #14P05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #Representation Theory (math.RT) #math.AG #math.RT #msc:11G15 #msc:14P05

paper · pdf · doi:10.48550/arxiv.math/0108103

arxiv created 2001/08/15 · openalex publication_date 2001/08/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The moduli space of principally polarized abelian varieties with real structure and with level N=4m structure (with m ≥ 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 GL(n, \mathbb R)/\mathbf O(N) (of positive definite symmetric matrices) by the principal congruence subgroup of level N in GL(n, \mathbb Z).

Related

• Level structures on abelian varieties, Kodaira dimensions, and Lang's conjecture
• Abelian surfaces with anti-holomorphic multiplication
• Irreducibility of the Siegel moduli spaces with parahoric level structure
• On the reduction of the Siegel moduli space of abelian varieties of dimension 3 with Iwahori level structure
• The Moduli Space of Abelian Varieties and the Singularities of the Theta Divisor