Multiplier Modules of extended Rees algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917042019368960 |
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| author | Ajit, Rahul |
| author_facet | Ajit, Rahul |
| contents | Given a local ring $(R, \mathfrak{m})$ and an ideal $\mathfrak{a}$ of positive height, we give a way of computing multiplier module ${J}(ω_{T}, t^{-λ})$ for the extended Rees algebra ${T} =R[\mathfrak{a} t, t^{-1}]$ for an ideal $\mathfrak{a}$ by proving a decomposition theorem for ${J}(ω_{T}, t^{-λ})$, (also see the works of Budur, Mustaţă and Saito). We compute the multiplier module ${J}(ω_{S}, (\mathfrak{a} \cdot {S})^λ)$ for the Rees algebra ${S} =R[\mathfrak{a} t]$ as well (also see the works of Hyry and Kotal-Kummini). We use these decompositions to understand relationships between associated graded rings, Rees and extended Rees algebras having rational singularities (also see the works of Hara, Watanabe, and Yoshida). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22074 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiplier Modules of extended Rees algebras Ajit, Rahul Algebraic Geometry Commutative Algebra 14F18, 13A30, 14E99 Given a local ring $(R, \mathfrak{m})$ and an ideal $\mathfrak{a}$ of positive height, we give a way of computing multiplier module ${J}(ω_{T}, t^{-λ})$ for the extended Rees algebra ${T} =R[\mathfrak{a} t, t^{-1}]$ for an ideal $\mathfrak{a}$ by proving a decomposition theorem for ${J}(ω_{T}, t^{-λ})$, (also see the works of Budur, Mustaţă and Saito). We compute the multiplier module ${J}(ω_{S}, (\mathfrak{a} \cdot {S})^λ)$ for the Rees algebra ${S} =R[\mathfrak{a} t]$ as well (also see the works of Hyry and Kotal-Kummini). We use these decompositions to understand relationships between associated graded rings, Rees and extended Rees algebras having rational singularities (also see the works of Hara, Watanabe, and Yoshida). |
| title | Multiplier Modules of extended Rees algebras |
| topic | Algebraic Geometry Commutative Algebra 14F18, 13A30, 14E99 |
| url | https://arxiv.org/abs/2510.22074 |