A Gorenstein criterion for strongly $F$-regular and log terminal singularities
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866910451207503872 |
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| author | Singh, Anurag K. Takagi, Shunsuke Varbaro, Matteo |
| author_facet | Singh, Anurag K. Takagi, Shunsuke Varbaro, Matteo |
| contents | A conjecture of Hirose, Watanabe, and Yoshida offers a characterization of when a standard graded strongly $F$-regular ring is Gorenstein, in terms of an $F$-pure threshold. We prove this conjecture under the additional hypothesis that the anti-canonical cover of the ring is Noetherian. Moreover, under this hypothesis on the anti-canonical cover, we give a similar criterion for when a normal $F$-pure (resp. log canonical) singularity is quasi-Gorenstein, in terms of an $F$-pure (resp. log canonical) threshold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1603_08422 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | A Gorenstein criterion for strongly $F$-regular and log terminal singularities Singh, Anurag K. Takagi, Shunsuke Varbaro, Matteo Commutative Algebra Algebraic Geometry A conjecture of Hirose, Watanabe, and Yoshida offers a characterization of when a standard graded strongly $F$-regular ring is Gorenstein, in terms of an $F$-pure threshold. We prove this conjecture under the additional hypothesis that the anti-canonical cover of the ring is Noetherian. Moreover, under this hypothesis on the anti-canonical cover, we give a similar criterion for when a normal $F$-pure (resp. log canonical) singularity is quasi-Gorenstein, in terms of an $F$-pure (resp. log canonical) threshold. |
| title | A Gorenstein criterion for strongly $F$-regular and log terminal singularities |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/1603.08422 |