Newton polygons and curve gonalities
Algebraic Geometry
2012-01-17 v2 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1106.3762,
title = {Newton polygons and curve gonalities},
author = {Wouter Castryck and Filip Cools},
journal= {arXiv preprint arXiv:1106.3762},
year = {2012}
}
Comments
29 pages, 18 figures; erratum at the end of the article