Blowup algebras of determinantal ideals in prime characteristic
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| author | De Stefani, Alessandro Montaño, Jonathan Núñez-Betancourt, Luis |
| author_facet | De Stefani, Alessandro Montaño, Jonathan Núñez-Betancourt, Luis |
| contents | We study when blowup algebras are $F$-split or strongly $F$-regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a symmetric matrix, and a Hankel matrix. We also study ideals of Pfaffians of a skew-symmetric matrix. We use these results to obtain bounds on the degrees of the defining equations for these algebras. We also prove that the limit of the normalized regularity of the symbolic powers of these ideals exists and that their depth stabilizes. Finally, we show that, for determinantal ideals, there exists a monomial order for which taking initial ideals commutes with taking symbolic powers. To obtain these results we develop the notion of $F$-split filtrations and symbolic $F$-split ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_00592 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Blowup algebras of determinantal ideals in prime characteristic De Stefani, Alessandro Montaño, Jonathan Núñez-Betancourt, Luis Commutative Algebra Algebraic Geometry 13A30, 13A35, 13A02, 13C15 We study when blowup algebras are $F$-split or strongly $F$-regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a symmetric matrix, and a Hankel matrix. We also study ideals of Pfaffians of a skew-symmetric matrix. We use these results to obtain bounds on the degrees of the defining equations for these algebras. We also prove that the limit of the normalized regularity of the symbolic powers of these ideals exists and that their depth stabilizes. Finally, we show that, for determinantal ideals, there exists a monomial order for which taking initial ideals commutes with taking symbolic powers. To obtain these results we develop the notion of $F$-split filtrations and symbolic $F$-split ideals. |
| title | Blowup algebras of determinantal ideals in prime characteristic |
| topic | Commutative Algebra Algebraic Geometry 13A30, 13A35, 13A02, 13C15 |
| url | https://arxiv.org/abs/2109.00592 |