Differential operators, anisotropy, and simplicial spheres
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916796105228288 |
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| author | Karu, Kalle Larson, Matt Stapledon, Alan |
| author_facet | Karu, Kalle Larson, Matt Stapledon, Alan |
| contents | We find identities involving differential operators in the generic artinian reduction of the Stanley-Reisner ring of a simplicial sphere in any positive characteristic. These identities generalize the characteristic 2 identities used by Papadakis and Petrotou to give a proof of the algebraic g-conjecture. We show that these identities are a shadow of an identity on the degree map, and we use them to prove the anisotropy of certain forms on the generic artinian reduction of the Stanley--Reisner ring and to prove weak Lefschetz results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04561 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential operators, anisotropy, and simplicial spheres Karu, Kalle Larson, Matt Stapledon, Alan Combinatorics Commutative Algebra 13F55 05E45 We find identities involving differential operators in the generic artinian reduction of the Stanley-Reisner ring of a simplicial sphere in any positive characteristic. These identities generalize the characteristic 2 identities used by Papadakis and Petrotou to give a proof of the algebraic g-conjecture. We show that these identities are a shadow of an identity on the degree map, and we use them to prove the anisotropy of certain forms on the generic artinian reduction of the Stanley--Reisner ring and to prove weak Lefschetz results. |
| title | Differential operators, anisotropy, and simplicial spheres |
| topic | Combinatorics Commutative Algebra 13F55 05E45 |
| url | https://arxiv.org/abs/2412.04561 |