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Nov 28, 2015 at 22:06 comment added Daniel Litt Sure; this follows from the surjectivity of the map $\pi_1(C)\to \pi_1(\text{Jac}(C))$, for example.
Nov 28, 2015 at 21:58 comment added nfdc23 Probably you should mention the small argument to justify that $C'$ is also connected.
Nov 14, 2015 at 18:17 history bounty ended gradstudent
Nov 6, 2015 at 13:49 vote accept gradstudent
Nov 6, 2015 at 4:33 vote accept gradstudent
Nov 6, 2015 at 13:49
Nov 6, 2015 at 4:31 history answered Daniel Litt CC BY-SA 3.0