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Nov 23, 2021 at 18:13 comment added Jef Great, thanks for your answer!
Nov 23, 2021 at 18:12 vote accept Jef
Nov 23, 2021 at 17:01 comment added abx @Jef: no. $dF$ is generically injective so its kernel is torsion, hence zero since $\mathscr{O}_C(-5)$ is torsion free.
Nov 23, 2021 at 11:50 comment added Jef Doesn't the exactness on the left of the first sequence require the smoothness of $C$?
Nov 23, 2021 at 8:34 history answered Sasha CC BY-SA 4.0