BCM-regularity of diagonal hypersurfaces and plus-pure thresholds in mixed characteristic
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916036300767232 |
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| author | Yamaguchi, Tatsuki |
| author_facet | Yamaguchi, Tatsuki |
| contents | We introduce a new method for computing plus-pure thresholds, a mixed-characteristic analogue of both log canonical thresholds and $F$-pure thresholds. We obtain some necessary conditions and some sufficient conditions for BCM-regularity of Fermat-type hypersurfaces. We also establish lower bounds for plus-pure thresholds of diagonal hypersurfaces in mixed characteristic. Furthermore, we give bounds for plus-pure thresholds of hypersurfaces in mixed characteristic $(0,2)$ using splitting-order sequences, introduced by Yoshikawa. As an application, we classify BCM-regular diagonal hypersurfaces in mixed characteristic $(0,2)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_22419 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | BCM-regularity of diagonal hypersurfaces and plus-pure thresholds in mixed characteristic Yamaguchi, Tatsuki Commutative Algebra Algebraic Geometry 13A35, 14B05, 14G45, 14F18 We introduce a new method for computing plus-pure thresholds, a mixed-characteristic analogue of both log canonical thresholds and $F$-pure thresholds. We obtain some necessary conditions and some sufficient conditions for BCM-regularity of Fermat-type hypersurfaces. We also establish lower bounds for plus-pure thresholds of diagonal hypersurfaces in mixed characteristic. Furthermore, we give bounds for plus-pure thresholds of hypersurfaces in mixed characteristic $(0,2)$ using splitting-order sequences, introduced by Yoshikawa. As an application, we classify BCM-regular diagonal hypersurfaces in mixed characteristic $(0,2)$. |
| title | BCM-regularity of diagonal hypersurfaces and plus-pure thresholds in mixed characteristic |
| topic | Commutative Algebra Algebraic Geometry 13A35, 14B05, 14G45, 14F18 |
| url | https://arxiv.org/abs/2605.22419 |