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Aug 16, 2013 at 1:35 comment added roy smith to add to this nice answer, note that the abel map induces one on every symmetric product X^(d)-->J, whose fibers are linear systems ≈ P^r, and hence whenever d > dimJ= g(X), there must be divisors of degree d that are linearly equivalent. In particular dim.h^0(D) ≥ g-d.
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Aug 11, 2013 at 15:40 history edited Darius Math CC BY-SA 3.0
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Aug 11, 2013 at 8:34 history answered Darius Math CC BY-SA 3.0