Graph Curve Matroids
| Autor: | Geiger, Alheydis, Kuehn, Kevin, Vlad, Raluca |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 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 |
| Databáze: | arXiv |
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