Diagonal F-thresholds for determinants and Pfaffians
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912881644142592 |
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| author | Betti, Barbara Raicu, Claudiu Romeo, Francesco Singh, Jyoti |
| author_facet | Betti, Barbara Raicu, Claudiu Romeo, Francesco Singh, Jyoti |
| contents | We compute the diagonal F-thresholds of determinantal hypersurfaces arising from a generic matrix and from a generic symmetric matrix, as well as of the Pfaffian hypersurface arising from a generic skew-symmetric matrix of even size. The main ingredient is a cohomology vanishing theorem for certain line bundles on flag varieties in characteristic $p$. In the cases of the generic matrix and the generic skew-symmetric matrix, we show that the diagonal F-threshold attains its minimal possible value, namely the negative of the a-invariant. The symmetric case is more subtle and relies in addition on a polynomiality result for representations afforded by cohomology, building on work of the second author with VandeBogert. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_05761 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diagonal F-thresholds for determinants and Pfaffians Betti, Barbara Raicu, Claudiu Romeo, Francesco Singh, Jyoti Commutative Algebra Algebraic Geometry Representation Theory Primary 13A35, 14M12, 14M15, 20G05, 20G10 We compute the diagonal F-thresholds of determinantal hypersurfaces arising from a generic matrix and from a generic symmetric matrix, as well as of the Pfaffian hypersurface arising from a generic skew-symmetric matrix of even size. The main ingredient is a cohomology vanishing theorem for certain line bundles on flag varieties in characteristic $p$. In the cases of the generic matrix and the generic skew-symmetric matrix, we show that the diagonal F-threshold attains its minimal possible value, namely the negative of the a-invariant. The symmetric case is more subtle and relies in addition on a polynomiality result for representations afforded by cohomology, building on work of the second author with VandeBogert. |
| title | Diagonal F-thresholds for determinants and Pfaffians |
| topic | Commutative Algebra Algebraic Geometry Representation Theory Primary 13A35, 14M12, 14M15, 20G05, 20G10 |
| url | https://arxiv.org/abs/2602.05761 |