Toric rings of signed posets and conic divisorial ideals via matroid theory
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917457908727808 |
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| author | Matsushita, Koji |
| author_facet | Matsushita, Koji |
| contents | We study conic divisorial ideals from the viewpoint of matroid theory and apply the resulting framework to toric rings arising from signed posets. For a toric ring, we describe the polytope representing divisor classes corresponding to conic divisorial ideals in terms of matroids. We then turn to the toric ring $R_P$ associated with a signed poset $P$. We compute the divisor class group and characterize the ($\mathbb{Q}$-)Gorenstein property of $R_P$ in terms of $P$. Moreover, we also construct a polytope characterizing the conic divisorial ideals of $R_P$. This recovers and extends previous results on Hibi rings to the setting of signed posets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02532 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toric rings of signed posets and conic divisorial ideals via matroid theory Matsushita, Koji Commutative Algebra Combinatorics Primary 13F65, Secondary 13C20, 05B35, 05C22 We study conic divisorial ideals from the viewpoint of matroid theory and apply the resulting framework to toric rings arising from signed posets. For a toric ring, we describe the polytope representing divisor classes corresponding to conic divisorial ideals in terms of matroids. We then turn to the toric ring $R_P$ associated with a signed poset $P$. We compute the divisor class group and characterize the ($\mathbb{Q}$-)Gorenstein property of $R_P$ in terms of $P$. Moreover, we also construct a polytope characterizing the conic divisorial ideals of $R_P$. This recovers and extends previous results on Hibi rings to the setting of signed posets. |
| title | Toric rings of signed posets and conic divisorial ideals via matroid theory |
| topic | Commutative Algebra Combinatorics Primary 13F65, Secondary 13C20, 05B35, 05C22 |
| url | https://arxiv.org/abs/2605.02532 |