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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.19018 |
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| _version_ | 1866909863186006016 |
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| author | Mantero, Paolo Nguyen, Vinh |
| author_facet | Mantero, Paolo Nguyen, Vinh |
| contents | Let $\M$ be a matroid, and let $I_{\M}$ be either the Stanley--Reisner or the cover ideal of $\M$. In this paper we prove that for any matroid $\M$ on $[n]$, any $\ell\in \ZZ_+$, and any squarefree monomial $N\in R=\kk[x_1,\ldots,x_n]$, the ideal $I_{\M}^{(\ell)}:N$, which we call a ``slightly mixed symbolic power" of $I_{\M}$, is always Cohen--Macaulay and locally glicci. As a corollary, we obtain that all symbolic powers $I_{\M}^{(\ell)}$ are locally glicci. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Slightly mixed symbolic powers of matroids are locally glicci Mantero, Paolo Nguyen, Vinh Commutative Algebra 13C40 Let $\M$ be a matroid, and let $I_{\M}$ be either the Stanley--Reisner or the cover ideal of $\M$. In this paper we prove that for any matroid $\M$ on $[n]$, any $\ell\in \ZZ_+$, and any squarefree monomial $N\in R=\kk[x_1,\ldots,x_n]$, the ideal $I_{\M}^{(\ell)}:N$, which we call a ``slightly mixed symbolic power" of $I_{\M}$, is always Cohen--Macaulay and locally glicci. As a corollary, we obtain that all symbolic powers $I_{\M}^{(\ell)}$ are locally glicci. |
| title | Slightly mixed symbolic powers of matroids are locally glicci |
| topic | Commutative Algebra 13C40 |
| url | https://arxiv.org/abs/2510.19018 |