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arXiv · 2311.02718

A note on dual abelian varieties

Aleksandra Borówka·Paweł Borówka
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Abstract

For any non-principal polarisation $D$, we explicitly construct $D$-polarised abelian variety $A$, such that its dual abelian variety is not (abstractly) isomorphic to $A$. For $\dim(A)>3$ the construction includes examples with submaximal Picard number equal to $(\dim(A)-1)^2+1$. As a corollary, we show that a very general non-principally polarised abelian variety is not isomorphic to its dual. Moreover, we show an example of an abelian variety that is isomorphic to its dual, yet it does not admit a principal polarisation.

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Aleksandra Borówka, Paweł Borówka. 2023-11-05. A note on dual abelian varieties. https://arxiv.org/abs/2311.02718

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