$p$-anisotropy on the moment curve for homology manifolds and cycles
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918192571482112 |
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| author | Adiprasito, Karim Hou, Kaiying Kiyohara, Daishi Koizumi, Daniel Stephenson, Monroe |
| author_facet | Adiprasito, Karim Hou, Kaiying Kiyohara, Daishi Koizumi, Daniel Stephenson, Monroe |
| contents | We prove that the Gorensteinification of the face ring of a cycle is totally $p$-anisotropic in characteristic $p$. In other words, given an appropriate Artinian reduction, it contains no nonzero $p$-isotropic elements. Moreover, we prove that the linear system of parameters can be chosen corresponding to a geometric realization with points on the moment curve. In particular, this implies that the parameters do not have to be chosen very generically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $p$-anisotropy on the moment curve for homology manifolds and cycles Adiprasito, Karim Hou, Kaiying Kiyohara, Daishi Koizumi, Daniel Stephenson, Monroe Combinatorics Commutative Algebra We prove that the Gorensteinification of the face ring of a cycle is totally $p$-anisotropic in characteristic $p$. In other words, given an appropriate Artinian reduction, it contains no nonzero $p$-isotropic elements. Moreover, we prove that the linear system of parameters can be chosen corresponding to a geometric realization with points on the moment curve. In particular, this implies that the parameters do not have to be chosen very generically. |
| title | $p$-anisotropy on the moment curve for homology manifolds and cycles |
| topic | Combinatorics Commutative Algebra |
| url | https://arxiv.org/abs/2502.05681 |