Trimming Five Generated Gorenstein Ideals
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929303376101376 |
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| author | Ferraro, Luigi Moore, W. Frank |
| author_facet | Ferraro, Luigi Moore, W. Frank |
| contents | Let $(R,\mathfrak{m},\Bbbk)$ be a regular local ring of dimension 3. Let $I$ be a Gorenstein ideal of $R$ of grade 3. It follows from a result of Buchsbaum and Eisenbud that there is a skew-symmetric matrix of odd size such that $I$ is generated by the sub-maximal pfaffians of this matrix. Let $J$ be the ideal obtained by multiplying some of the pfaffian generators of $I$ by $\mathfrak{m}$; we say that $J$ is a trimming of $I$. In a previous work, the first author and A. Hardesty constructed an explicit free resolution of $R/J$ and computed a DG algebra structure on this resolution. They utilized these products to analyze the Tor algebra of such trimmed ideals. Missing from their result was the case where $I$ is five generated. In this paper we address this case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_03601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Trimming Five Generated Gorenstein Ideals Ferraro, Luigi Moore, W. Frank Commutative Algebra 13C05, 13D02, 13D07, 13H10 Let $(R,\mathfrak{m},\Bbbk)$ be a regular local ring of dimension 3. Let $I$ be a Gorenstein ideal of $R$ of grade 3. It follows from a result of Buchsbaum and Eisenbud that there is a skew-symmetric matrix of odd size such that $I$ is generated by the sub-maximal pfaffians of this matrix. Let $J$ be the ideal obtained by multiplying some of the pfaffian generators of $I$ by $\mathfrak{m}$; we say that $J$ is a trimming of $I$. In a previous work, the first author and A. Hardesty constructed an explicit free resolution of $R/J$ and computed a DG algebra structure on this resolution. They utilized these products to analyze the Tor algebra of such trimmed ideals. Missing from their result was the case where $I$ is five generated. In this paper we address this case. |
| title | Trimming Five Generated Gorenstein Ideals |
| topic | Commutative Algebra 13C05, 13D02, 13D07, 13H10 |
| url | https://arxiv.org/abs/2404.03601 |