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Jan 16, 2016 at 19:55 answer added Jason Starr timeline score: 2
Jan 16, 2016 at 14:19 comment added Jason Starr I just want to clarify the question. There exists a finite, closed subgroup scheme $\Gamma \subset \text{Prym}(C/C')$ and a flat morphism of group schemes $\pi:J(C)\to \text{Prym}(C/C')/\Gamma$ that restricts to the quotient morphism $q:\text{Prym}(C/C')\to\text{Prym}(C/C')/\Gamma$. Certainly the composition of $\pi$ with the Abel map $\text{sym}^d(C)\to J(C)$ is surjective. Are you asking whether this surjection factors through $q$?
Jan 16, 2016 at 10:56 history asked Dimitri Koshelev CC BY-SA 3.0