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Sep 6, 2018 at 8:06 comment added Sasha @Hephaistos: You are right.
Sep 4, 2018 at 14:47 history edited Hephaistos CC BY-SA 4.0
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Sep 4, 2018 at 14:10 history edited Hephaistos CC BY-SA 4.0
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Sep 4, 2018 at 13:54 comment added Mohsen Karkheiran The specific example I have in mind is genus 1 reducible curve. Specially $I_N$
Sep 4, 2018 at 13:50 comment added Mohsen Karkheiran I can refer to this paper arxiv.org/abs/math/0410393, right before Proposition 2.3, the author mentions that if X is projective, and $C_i$ are the irreducible components then (taken from a paper or book by Seshadri) the representation exists. Unfortunately, I don't have access to the reference by Seshadri to read the proof...
Sep 4, 2018 at 13:36 history answered Hephaistos CC BY-SA 4.0