An Isomorphism Between Moduli Spaces of Abelian Varieties

Details An Isomorphism Between Moduli Spaces of Abelian Varieties An Isomorphism Between Moduli Spaces of Abelian Varieties

2002-04-22

arxiv.org/abs/math/0204260v1

Mathematics

Algebraic Geometry

7 pages

Scientific paper

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 $\mathcal A_{(d_1,\frac{d_1d_g}{d_{g-1}},...,\frac{d_1d_g}{d_2},d_g)}$ are canonically isomorphic.

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