The $F$-regularity of algebraic sets related to commutator matrices
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916518844956672 |
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| author | Chau, Trung |
| author_facet | Chau, Trung |
| contents | We study the algebraic sets of pairs of matrices defined by the vanishing of the anti-diagonal as well as the cross-diagonal of their commutator matrix. We prove that, over a field of prime characterisitic, the coordinate ring of the latter is always $F$-regular and, with exactly one exception, so is that of the former, thus proving a conjecture of Kadyrsizova and Yerlanov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15487 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The $F$-regularity of algebraic sets related to commutator matrices Chau, Trung Commutative Algebra Algebraic Geometry 13A35 (Primary), 14G17, 14M10, 14M99 We study the algebraic sets of pairs of matrices defined by the vanishing of the anti-diagonal as well as the cross-diagonal of their commutator matrix. We prove that, over a field of prime characterisitic, the coordinate ring of the latter is always $F$-regular and, with exactly one exception, so is that of the former, thus proving a conjecture of Kadyrsizova and Yerlanov. |
| title | The $F$-regularity of algebraic sets related to commutator matrices |
| topic | Commutative Algebra Algebraic Geometry 13A35 (Primary), 14G17, 14M10, 14M99 |
| url | https://arxiv.org/abs/2305.15487 |