English

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

R2 v1 2026-06-21T18:24:35.467Z