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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. What is the reasoning behind this statement?
I did find a paper which had a generalization of the Torelli theorem i. Even with this, I guess it doesn't really finish the question since there are a lot of principally polarized abelian varieties that aren't isomorphic or even isogenous to a Jacobian.
Is there a simpler reason why the statement should be true? If so, how should I think about this? Also, does paper mentioned above actually apply to the situation that I'm thinking about?
Update : It should be made clear that we are probably taking the product polarization of the product of principally polarized abelian varieties mentioned in the old MSE question. Otherwise, it may be possible to get a Jacobian which is isomorphic to a product of Jacobians.
This still doesn't explain why arbitrary products of principally polarized abelian varieties with the product polarization would be bad. Sign up to join this community. The best answers are voted up and rise to the top.
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