Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911539454279680 |
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| author | Pak, Igor Shapiro, Boris Smirnov, Ilya Yoshida, Ken-ichi |
| author_facet | Pak, Igor Shapiro, Boris Smirnov, Ilya Yoshida, Ken-ichi |
| contents | We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart polynomials of integer polytopes. In consequence, we prove that the Hilbert-Kunz multiplicity of quadrics of fixed characteristic is a decreasing function of dimension and recover results of Trivedi and Gessel-Monsky on the behaviour of said Hilbert-Kunz multiplicity as a function of characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hilbert-Kunz multiplicity of quadrics via Ehrhart theory Pak, Igor Shapiro, Boris Smirnov, Ilya Yoshida, Ken-ichi Commutative Algebra Algebraic Geometry Combinatorics We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart polynomials of integer polytopes. In consequence, we prove that the Hilbert-Kunz multiplicity of quadrics of fixed characteristic is a decreasing function of dimension and recover results of Trivedi and Gessel-Monsky on the behaviour of said Hilbert-Kunz multiplicity as a function of characteristic. |
| title | Hilbert-Kunz multiplicity of quadrics via Ehrhart theory |
| topic | Commutative Algebra Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2508.17915 |