Ladder determinantal varieties and their symbolic blowups
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912818968657920 |
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| author | De Stefani, Alessandro Montaño, Jonathan Núñez-Betancourt, Luis Seccia, Lisa Varbaro, Matteo |
| author_facet | De Stefani, Alessandro Montaño, Jonathan Núñez-Betancourt, Luis Seccia, Lisa Varbaro, Matteo |
| contents | In this article we show that the symbolic Rees algebra of a mixed ladder determinantal ideal is strongly $F$-regular. Furthermore, we prove that the symbolic associated graded algebra of a mixed ladder determinantal ideal is $F$-pure. The latter implies that mixed ladder determinantal rings are $F$-pure. We also show that ideals of the poset of minors of a generic matrix give rise to $F$-pure algebras with straightening law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18167 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ladder determinantal varieties and their symbolic blowups De Stefani, Alessandro Montaño, Jonathan Núñez-Betancourt, Luis Seccia, Lisa Varbaro, Matteo Commutative Algebra Algebraic Geometry Combinatorics In this article we show that the symbolic Rees algebra of a mixed ladder determinantal ideal is strongly $F$-regular. Furthermore, we prove that the symbolic associated graded algebra of a mixed ladder determinantal ideal is $F$-pure. The latter implies that mixed ladder determinantal rings are $F$-pure. We also show that ideals of the poset of minors of a generic matrix give rise to $F$-pure algebras with straightening law. |
| title | Ladder determinantal varieties and their symbolic blowups |
| topic | Commutative Algebra Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2305.18167 |