Graph Curve Matroids
Abstract
We introduce a new class of matroids, called graph curve matroids. A graph curve matroid is associated to a graph and defined on the vertices of the graph as a ground set. We prove that these matroids provide a combinatorial description of hyperplane sections of degenerate canonical curves in algebraic geometry. Our focus lies on graphs that are 2-connected and trivalent, which define identically self-dual graph curve matroids, but we also develop generalizations. Finally, we provide an algorithm to compute the graph curve matroid associated to a given graph, as well as an implementation and data of examples that can be used in Macaulay2.
Keywords
Cite
@article{arxiv.2311.08332,
title = {Graph Curve Matroids},
author = {Alheydis Geiger and Kevin Kuehn and Raluca Vlad},
journal= {arXiv preprint arXiv:2311.08332},
year = {2024}
}
Comments
15 pages, 4 figures, comments are welcome. V2: we included most of the proofs that were omitted in the original version and give more details in general