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Aug 12, 2019 at 11:54 comment added abx No, there is no nontrivial map from an abelian variety to a curve of genus $\geq 2$ (as Aryan said already).
Aug 12, 2019 at 11:30 comment added PSUN Thanks. Is there exist any map from $J\to D\times \theta$? Just by using the fact $D.\theta=1$, where $D$ is effective divisor. I am very sorry if I am asking very silly question.
Aug 12, 2019 at 9:27 history answered abx CC BY-SA 4.0