Duality and the equations of Rees rings and tangent algebras
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909220951031808 |
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| author | Weaver, Matthew |
| author_facet | Weaver, Matthew |
| contents | Let $E$ be a module of projective dimension one over a Noetherian ring $R$ and consider its Rees algebra $\mathcal{R}(E)$. We study this ring as a quotient of the symmetric algebra $\mathcal{S}(E)$ and consider the ideal $\mathcal{A}$ defining this quotient. In the case that $\mathcal{S}(E)$ is a complete intersection ring, we employ a duality between $\mathcal{A}$ and $\mathcal{S}(E)$ in order to study the Rees ring $\mathcal{R}(E)$ in multiple settings. In particular, when $R$ is a complete intersection ring defined by quadrics, we consider its module of Kähler differentials $Ω_{R/k}$ and its associated tangent algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality and the equations of Rees rings and tangent algebras Weaver, Matthew Commutative Algebra 13A30 Let $E$ be a module of projective dimension one over a Noetherian ring $R$ and consider its Rees algebra $\mathcal{R}(E)$. We study this ring as a quotient of the symmetric algebra $\mathcal{S}(E)$ and consider the ideal $\mathcal{A}$ defining this quotient. In the case that $\mathcal{S}(E)$ is a complete intersection ring, we employ a duality between $\mathcal{A}$ and $\mathcal{S}(E)$ in order to study the Rees ring $\mathcal{R}(E)$ in multiple settings. In particular, when $R$ is a complete intersection ring defined by quadrics, we consider its module of Kähler differentials $Ω_{R/k}$ and its associated tangent algebras. |
| title | Duality and the equations of Rees rings and tangent algebras |
| topic | Commutative Algebra 13A30 |
| url | https://arxiv.org/abs/2406.06766 |