The dth symmetric power Cd of a smooth complex projective curve (or compact Riemann surface) C is a parameter space for effective divisors of degree d on C, so that the theory of degree-d maps from C to projective space is encoded in the subvarieties of Cd and the relations amongst them. We give a complete description of the cone of codimension-1 subvarieties of Cg–1 when C is a general curve of genus g ≥ 4, as well as new bounds for the case Cd in the range ([special characters omitted], g – 2]. We also give new information on the movable cone of Cd and the volume function of Cg–1.
|School:||State University of New York at Stony Brook|
|School Location:||United States -- New York|
|Source:||DAI-B 69/12, Dissertation Abstracts International|
|Keywords:||Cone, Curves, Symmetric powers|
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