An Isomorphism Between Moduli Spaces of Abelian Varieties

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 ${\mathcal{A}}_{(d_1,...,d_g)}$ and ${\mathcal{A}}_{(d_1,\frac{d_1{d}_g}{d_{g-1}},...,\frac{d_1{d}_g}{d_2},d_g)}$ are canonically isomorphic.

7 pages

Cited by in corpus (7)

• Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds
• Global Prym-Torelli for double coverings ramified in at least 6 points
• Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)
• The fibers of the ramified Prym map
• The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds
• Derived equivalent conjugate K3 surfaces
• Divisors of ${\mathcal{A}}_4^{(1,1,2,2)}$