An Isomorphism Between Moduli Spaces of Abelian Varieties

2002/04/22 by Ch. Birkenhake, Herbert Lange, Birkenhake, Ch. +2
Mathematics · #14K05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14K05

paper · pdf · doi:10.48550/arxiv.math/0204260

7 pages

arxiv created 2002/04/22 · openalex publication_date 2002/04/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a previous paper we showed that for every polarization on an abelian variety there is a dual polarization on the dual abelian variety. In this note we extend this notion of duality to families of polarized abelian varieties. As a main consequence we obtain an involution on the set of moduli spaces of polarized abelian varieties of dimension g. In particular, the moduli spaces \mathcal A_(d1,...,dg) and \mathcal A_(d₁,\fracd₁d_gd_g-1,...,(d₁d_g)/(d₂),d_g) are canonically isomorphic.

Related

• The Moduli Space of Abelian Varieties and the Singularities of the Theta Divisor
• Siegel coordinates and moduli spaces for morphisms of abelian varieties
• A note on dual abelian varieties
• Polarizations on abelian varieties
• Geometry of A_g and Its Compactifications