The arithmetic rank of determinantal nullcones
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917277313531904 |
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| author | Jeffries, Jack Pandey, Vaibhav Singh, Anurag K. Walther, Uli |
| author_facet | Jeffries, Jack Pandey, Vaibhav Singh, Anurag K. Walther, Uli |
| contents | We compute the arithmetic rank as well as the local/étale cohomological dimension of nullcone ideals arising from the classical actions of the symplectic group, the general linear group, and the orthogonal group. We use these calculations to establish striking vanishing results for local cohomology modules supported at these nullcone ideals; this is achieved via a careful analysis of the critical local cohomology modules. The vanishing theorems that we prove are sharp in various respects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The arithmetic rank of determinantal nullcones Jeffries, Jack Pandey, Vaibhav Singh, Anurag K. Walther, Uli Commutative Algebra Algebraic Geometry Representation Theory Primary 13A50, Secondary 13C40, 13D45, 13F20, 14F20, 55N10 We compute the arithmetic rank as well as the local/étale cohomological dimension of nullcone ideals arising from the classical actions of the symplectic group, the general linear group, and the orthogonal group. We use these calculations to establish striking vanishing results for local cohomology modules supported at these nullcone ideals; this is achieved via a careful analysis of the critical local cohomology modules. The vanishing theorems that we prove are sharp in various respects. |
| title | The arithmetic rank of determinantal nullcones |
| topic | Commutative Algebra Algebraic Geometry Representation Theory Primary 13A50, Secondary 13C40, 13D45, 13F20, 14F20, 55N10 |
| url | https://arxiv.org/abs/2509.20470 |