Graph Curve Matroids
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913456791224320 |
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| author | Geiger, Alheydis Kuehn, Kevin Vlad, Raluca |
| author_facet | Geiger, Alheydis Kuehn, Kevin Vlad, Raluca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08332 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Graph Curve Matroids Geiger, Alheydis Kuehn, Kevin Vlad, Raluca Combinatorics Algebraic Geometry 05E14 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. |
| title | Graph Curve Matroids |
| topic | Combinatorics Algebraic Geometry 05E14 |
| url | https://arxiv.org/abs/2311.08332 |