Newton polygons and curve gonalities

Details Newton polygons and curve gonalities Newton polygons and curve gonalities

2011-06-19

arxiv.org/abs/1106.3762v2

Mathematics

Algebraic Geometry

29 pages, 18 figures; erratum at the end of the article

Scientific paper

We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number of special cases. One proof technique uses recent work of M. Baker on linear systems on graphs, by means of which we reduce our conjecture to a purely combinatorial statement.

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