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arXiv · 2605.22419

BCM-regularity of diagonal hypersurfaces and plus-pure thresholds in mixed characteristic

Tatsuki Yamaguchi
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Abstract

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 $(0,2)$.

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Tatsuki Yamaguchi. 2026-05-21. BCM-regularity of diagonal hypersurfaces and plus-pure thresholds in mixed characteristic. https://arxiv.org/abs/2605.22419

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