Limit $F$-signature functions of two-variable binomial hypersurfaces
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912347051786240 |
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| author | Brosowsky, Anna Coskun, Izzet Pande, Suchitra Tucker, Kevin |
| author_facet | Brosowsky, Anna Coskun, Izzet Pande, Suchitra Tucker, Kevin |
| contents | The $F$-signature is a fundamental numerical invariant of singularities in positive characteristic. Its positivity detects strong $F$-regularity, an important class of singularities related to KLT singularities in characteristic zero. In this paper, we compute the limiting $F$-signature function of binomial and other related hypersurfaces in two variables as the characteristic $p \to \infty$. In particular, we show it is a piecewise polynomial function, and relate it to the normalized volume. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit $F$-signature functions of two-variable binomial hypersurfaces Brosowsky, Anna Coskun, Izzet Pande, Suchitra Tucker, Kevin Commutative Algebra Algebraic Geometry 13A35 (Primary) 13P10, 14B05 (Secondary) The $F$-signature is a fundamental numerical invariant of singularities in positive characteristic. Its positivity detects strong $F$-regularity, an important class of singularities related to KLT singularities in characteristic zero. In this paper, we compute the limiting $F$-signature function of binomial and other related hypersurfaces in two variables as the characteristic $p \to \infty$. In particular, we show it is a piecewise polynomial function, and relate it to the normalized volume. |
| title | Limit $F$-signature functions of two-variable binomial hypersurfaces |
| topic | Commutative Algebra Algebraic Geometry 13A35 (Primary) 13P10, 14B05 (Secondary) |
| url | https://arxiv.org/abs/2504.18656 |