The F-pure threshold versus the a-invariant for standard graded rings
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908480843022336 |
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| author | Pande, Suchitra |
| author_facet | Pande, Suchitra |
| contents | Hirose, Watanabe and Yoshida conjectured a criterion for a standard graded strongly $F$-regular ring to be Gorenstein in terms of the $F$-pure threshold. We complete the proof of this conjecture. We also prove natural extensions of the conjecture to section rings of normal, $F$-split projective varieties with respect to globally generated ample divisors. Our proof exploits the geometry of the Proj of the graded ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The F-pure threshold versus the a-invariant for standard graded rings Pande, Suchitra Commutative Algebra Algebraic Geometry 13A35, 13H10 Hirose, Watanabe and Yoshida conjectured a criterion for a standard graded strongly $F$-regular ring to be Gorenstein in terms of the $F$-pure threshold. We complete the proof of this conjecture. We also prove natural extensions of the conjecture to section rings of normal, $F$-split projective varieties with respect to globally generated ample divisors. Our proof exploits the geometry of the Proj of the graded ring. |
| title | The F-pure threshold versus the a-invariant for standard graded rings |
| topic | Commutative Algebra Algebraic Geometry 13A35, 13H10 |
| url | https://arxiv.org/abs/2508.04940 |