Graphs of gonality three
Combinatorics
2020-03-06 v3 Algebraic Geometry
Abstract
In 2013, Chan classified all metric hyperelliptic graphs, proving that divisorial gonality and geometric gonality are equivalent in the hyperelliptic case. We show that such a classification extends to combinatorial graphs of divisorial gonality three, under certain edge- and vertex-connectivity assumptions. We also give a construction for graphs of divisorial gonality three, and provide conditions for determining when a graph is not of divisorial gonality three.
Keywords
Cite
@article{arxiv.1810.08665,
title = {Graphs of gonality three},
author = {Ivan Aidun and Frances Dean and Ralph Morrison and Teresa Yu and Julie Yuan},
journal= {arXiv preprint arXiv:1810.08665},
year = {2020}
}
Comments
19 pages, 13 figures; corrected statements of Theorems 1.2 and 4.1, as well as material in Section 4