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Oct 24, 2017 at 8:07 comment added S. Carnahan @rtz Sorry, my answer was poorly worded, and I should have emphasized something other than the nontriviality of $\Omega^{1/2}$ in the non-affine case. Unfortunately, I do not know enough in general to either make the triviality claim or say it is false. There are plenty of punctured Riemann surfaces of positive genus with nontrivial $Pic^0$, so I don't know an easy way to back up such a claim.
Oct 24, 2017 at 4:04 comment added stupid_question_bot I'm reading your answer again, and I'm wondering - Are you claiming that when $\Gamma$ is torsion-free, then $\Omega^{1/2}$ is the trivial bundle? Why is that true?
Oct 2, 2016 at 2:59 vote accept stupid_question_bot
Oct 2, 2016 at 2:15 history answered S. Carnahan CC BY-SA 3.0