I know that if $X$ is an abelian variety, then it need not be isomorphic to its dual. But I don't know any example: Jacobians, elliptic curves etc are all isomorphic to their duals. Does anyone know an example. Also is $X$ homeomorphic to its dual?
Regarding the dual of an abelian variety
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algebraic-geometry
abelian-varieties
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1For the second part, abelian varieties are tori, so in a given dimension they are all diffeomorphic. I don't know a nice example for the first part. – 2017-01-24
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0@Nefertiti thanks for the comment! it is helpful to me – 2017-01-24
1 Answers
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An abelian variety is isomorphic to its dual if and only if it has a principal polarization. Examples of abelian varieties which do not have a principal polarization are given in the answers to this MO question:
https://mathoverflow.net/questions/16992/non-principally-polarized-complex-abelian-varieties