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LSpice
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You may find this paper of Hartshorne to be helpful.

You may find the paper Generalized divisors on Gorenstein curves and a theorem of Noether of Hartshorne to be helpful.

broken link fixed, cf. https://meta.mathoverflow.net/q/5301/70594
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Glorfindel
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You may find this paper of Hartshorne to be helpful.

You may find this paper of Hartshorne to be helpful.

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Vivek Shende
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You may find this paper of Hartshorne to be helpful.