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<p>We introduce a new class of matroids, called <i>graph curve matroids</i>. 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-edge-connected and trivalent. These define <i>identically self-dual</i> graph curve matroids, but we also develop generalizations. Finally, we provide an implementation in <Emphasis FontCategory="NonProportional">Macaulay2</Emphasis> and data of examples.</p>

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Graph curve matroids

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月19日

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  • Alheydis Geiger,
  • Kevin Kühn,
  • Raluca Vlad

摘要

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-edge-connected and trivalent. These define identically self-dual graph curve matroids, but we also develop generalizations. Finally, we provide an implementation in Macaulay2 and data of examples.