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Feb 4, 2015 at 0:41 history edited Peter Crooks CC BY-SA 3.0
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Feb 4, 2015 at 0:40 comment added Peter Crooks Yes, "in general" means genus $>0$ in this case. I'll record this above to clarify.
Feb 4, 2015 at 0:39 comment added ACL Just to clarify the adverb "in general", let me point out the trivial and only counterexample: What you say is OK, unless $X$ is Riemann sphere, in which case the kernel of $Pic(X)\to\mathbf Z$ is zero.
Feb 3, 2015 at 15:27 history edited Peter Crooks CC BY-SA 3.0
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Feb 3, 2015 at 15:03 history edited Peter Crooks CC BY-SA 3.0
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Feb 3, 2015 at 13:17 vote accept John Robertson
Feb 3, 2015 at 13:06 history answered Peter Crooks CC BY-SA 3.0