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3 votes

Is every abelian variety a subvariety of a Jacobian?

Let $A^*=Pic^0(A)$ and apply $Pic^0$ to a surjective homomorphism $J\to A^*$. Added: as noted, the existence of a surjective homomorphism goes back to a theorem of Matsusaka. For the proof, see Milne, …
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