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arXiv · 1603.08856

Brill-Noether varieties of k-gonal curves

Nathan Pflueger
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Abstract

We consider a general curve of fixed gonality k and genus g. We propose an estimate for the dimension of the variety $W^r_d(C)$ of special linear series on C, by solving an analogous problem in tropical geometry. Using work of Coppens and Martens, we prove that this estimate is exactly correct if k is at least g/5 + 2, and is an upper bound in all other cases. We also completely characterize the cases in which $W^r_d(C)$ has the same dimension as for a general curve of genus g.

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Nathan Pflueger. 2016-03-29. Brill-Noether varieties of k-gonal curves. https://doi.org/10.1016/j.aim.2017.01.027

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