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Bibliographic Details
Main Authors: Borówka, Aleksandra, Borówka, Paweł
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2311.02718
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Table of Contents:
  • 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.