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

Fuente: arXiv
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Main Author: Yamaguchi, Tatsuki
Format: Preprint
Published: 2026
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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
id 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