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Let X be an algebraic curve and c be the Clifford index of X. When c is small (e.g c=1), what is the classification of the line bundle who computes c?

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I know this is an old question (ok, two weeks, whatever) but my guess as to why you haven't gotten any responses is that your question is terribly vague. What are you looking for exactly? A means of constructing a line bundle achieving the bound? Also, you've given no motivation whatsoever, merely asked a hard-to-follow question. I'll gladly attempt to answer the question, once I'm more certain of what it is. – Charles Siegel Jan 7 at 14:36

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