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An isomorphism between moduli spaces of abelian varieties

✍ Scribed by Christina Birkenhake; Herbert Lange

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
111 KB
Volume
253
Category
Article
ISSN
0025-584X

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✦ Synopsis

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 $ {\cal A}_{(d_{1}, \ldots, d_{g})} $ and $ {\cal A}_{\left( d_1, {{d_{1}d_{g} \over {d_{g-1}}}, \ldots, {d_{1}d_{g} \over {d_{2}}}}, d_{g}\right)} $ are canonically isomorphic.

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