Brill-Noether theory of curves on toric surfaces

Geoffrey Degener Smith

Brill-Noether theory of curves on toric surfaces

Algebraic Geometry 2014-04-01 v2

Authors: Geoffrey Degener Smith

Abstract

A Laurent polynomial $f$ in two variables naturally describes a projective curve $C(f)$ on a toric surface. We show that if $C(f)$ is a smooth curve of genus at least 7, then $C(f)$ is not Brill-Noether general. To accomplish this, we classify all Newton polygons that admit such curves whose divisors all have nonnegative Brill-Noether number.

Keywords

Brill-Noether theory toric surfaces Laurent polynomial Newton polygons genus divisors Brill-Noether number

Cite

@article{arxiv.1403.2317,
  title  = {Brill-Noether theory of curves on toric surfaces},
  author = {Geoffrey Degener Smith},
  journal= {arXiv preprint arXiv:1403.2317},
  year   = {2014}
}

Comments

10 pages, 4 figures; changed formatting, added contact information

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