A duality theorem for the ic-resurgence of edge ideals
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929237261287424 |
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| author | Villarreal, Rafael H. |
| author_facet | Villarreal, Rafael H. |
| contents | The aim of this work is to use linear programming and polyhedral geometry to prove a duality formula for the ic-resurgence of edge ideals. We show that the ic-resurgence of the edge ideal $I$ of a clutter $\mathcal{C}$ and the ic-resurgence of the edge ideal $I^\vee$ of the blocker $\mathcal{C}^\vee$ of $\mathcal{C}$ coincide. If $\mathcal{C}$ is the clutter of bases of certain uniform matroids, we recover a formula for the resurgence of $I$, and if $\mathcal{C}$ is a connected non-bipartite graph with a perfect matching, we show a formula for the Waldschmidt constant of $I^\vee$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_01268 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A duality theorem for the ic-resurgence of edge ideals Villarreal, Rafael H. Commutative Algebra Combinatorics 13C70, 13F20, 13F55, 05E40 The aim of this work is to use linear programming and polyhedral geometry to prove a duality formula for the ic-resurgence of edge ideals. We show that the ic-resurgence of the edge ideal $I$ of a clutter $\mathcal{C}$ and the ic-resurgence of the edge ideal $I^\vee$ of the blocker $\mathcal{C}^\vee$ of $\mathcal{C}$ coincide. If $\mathcal{C}$ is the clutter of bases of certain uniform matroids, we recover a formula for the resurgence of $I$, and if $\mathcal{C}$ is a connected non-bipartite graph with a perfect matching, we show a formula for the Waldschmidt constant of $I^\vee$. |
| title | A duality theorem for the ic-resurgence of edge ideals |
| topic | Commutative Algebra Combinatorics 13C70, 13F20, 13F55, 05E40 |
| url | https://arxiv.org/abs/2203.01268 |