Cohomological support varieties for monomial ideals
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911726087176192 |
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| author | Fagerstrom, Kara Faur, Julianne Katz, Benjamin Sundaram, Kesavan Mohana Stern, Stephen Watson, Ryan |
| author_facet | Fagerstrom, Kara Faur, Julianne Katz, Benjamin Sundaram, Kesavan Mohana Stern, Stephen Watson, Ryan |
| contents | Let $R$ be a local or positively graded ring with a regular presentation $R \cong Q/I$ where $I$ is a monomial ideal generated by $n$ elements on a regular sequence. In Briggs-Grifo-Pollitz (2025), the authors classify the cohomological support varieties $\mathcal{V}_R(R)$ for $n \leqslant 5$. In this paper we extend their results to classify the varieties that can occur as $\mathcal{V}_R(R)$ for $n=6$. Moreover, we provide two families of rings, one realizing cohomological support varieties of unbounded codimension, the other realizing an unbounded number of components. Finally, we answer a question of Gintz (2026) about the varieties that occur as $\mathcal{V}_R(R)$ where $I$ is given by the edge ideal of a cycle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_29103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cohomological support varieties for monomial ideals Fagerstrom, Kara Faur, Julianne Katz, Benjamin Sundaram, Kesavan Mohana Stern, Stephen Watson, Ryan Commutative Algebra Combinatorics 13D99 (Primary) 05E40 (Secondary) Let $R$ be a local or positively graded ring with a regular presentation $R \cong Q/I$ where $I$ is a monomial ideal generated by $n$ elements on a regular sequence. In Briggs-Grifo-Pollitz (2025), the authors classify the cohomological support varieties $\mathcal{V}_R(R)$ for $n \leqslant 5$. In this paper we extend their results to classify the varieties that can occur as $\mathcal{V}_R(R)$ for $n=6$. Moreover, we provide two families of rings, one realizing cohomological support varieties of unbounded codimension, the other realizing an unbounded number of components. Finally, we answer a question of Gintz (2026) about the varieties that occur as $\mathcal{V}_R(R)$ where $I$ is given by the edge ideal of a cycle. |
| title | Cohomological support varieties for monomial ideals |
| topic | Commutative Algebra Combinatorics 13D99 (Primary) 05E40 (Secondary) |
| url | https://arxiv.org/abs/2605.29103 |