{
  "id": "2311.08332",
  "version": "v1",
  "published": "2023-11-14T17:25:05.000Z",
  "updated": "2023-11-14T17:25:05.000Z",
  "title": "Graph Curve Matroids",
  "authors": [
    "Alheydis Geiger",
    "Kevin Kuehn",
    "Raluca Vlad"
  ],
  "comment": "12 pages, 3 figures, comments are welcome",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-14T17:25:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E14"
    ],
    "keywords": [
      "define identically self-dual graph curve",
      "identically self-dual graph curve matroids",
      "combinatorial description",
      "degenerate canonical curves",
      "hyperplane sections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}