Maximal minors of $1$-generic matrices have rational singularities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916787533119488 |
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| author | Chau, Trung Kummini, Manoj |
| author_facet | Chau, Trung Kummini, Manoj |
| contents | We show that the quotient ring by the ideal of maximal minors of a $1$-generic matrix has rational singularities. This answers a conjecture of Eisenbud (1988) that such rings are normal, and generalizes a result of Conca, Mostafazadehfard, Singh and Varbaro (2018) that generic Hankel determinantal rings have rational singularities in characteristic zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal minors of $1$-generic matrices have rational singularities Chau, Trung Kummini, Manoj Commutative Algebra Algebraic Geometry 13C40, 14M12, 13D02 We show that the quotient ring by the ideal of maximal minors of a $1$-generic matrix has rational singularities. This answers a conjecture of Eisenbud (1988) that such rings are normal, and generalizes a result of Conca, Mostafazadehfard, Singh and Varbaro (2018) that generic Hankel determinantal rings have rational singularities in characteristic zero. |
| title | Maximal minors of $1$-generic matrices have rational singularities |
| topic | Commutative Algebra Algebraic Geometry 13C40, 14M12, 13D02 |
| url | https://arxiv.org/abs/2506.08385 |