Two-vertex generators of Jacobians of graphs
Combinatorics
2017-09-12 v2 Algebraic Geometry
Abstract
We give necessary and sufficient conditions under which the Jacobian of a graph is generated by a divisor that is the difference of two vertices. This answers a question posed by Becker and Glass and allows us to prove various other propositions about the order of divisors that are the difference of two vertices. We conclude with some conjectures about these divisors on random graphs and support them with empirical evidence.
Cite
@article{arxiv.1708.03069,
title = {Two-vertex generators of Jacobians of graphs},
author = {David Brandfonbrener and Pat Devlin and Netanel Friedenberg and Yuxuan Ke and Steffen Marcus and Henry Reichard and Ethan Sciamma},
journal= {arXiv preprint arXiv:1708.03069},
year = {2017}
}
Comments
15 pages, small edits for typos and clarity, added references, added author institutional and contact information