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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.18989 |
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| _version_ | 1866909232449716224 |
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| author | Fan, Feifei |
| author_facet | Fan, Feifei |
| contents | The generic anisotropy is an important property in the study of Stanley-Reisner rings of homology spheres, which was introduced by Papadakis and Petrotou. This property can be used to prove the strong Lefschetz property as well as McMullen's $g$-conjecture for homology spheres. It is conjectured that for an arbitrary field $\mathbb{F}$, any $\mathbb{F}$-homology sphere is generically anisotropic over $\mathbb{F}$. In this paper, we prove this conjecture for all strongly edge decomposable spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The generic anisotropy of strongly edge decomposable spheres Fan, Feifei Combinatorics Commutative Algebra The generic anisotropy is an important property in the study of Stanley-Reisner rings of homology spheres, which was introduced by Papadakis and Petrotou. This property can be used to prove the strong Lefschetz property as well as McMullen's $g$-conjecture for homology spheres. It is conjectured that for an arbitrary field $\mathbb{F}$, any $\mathbb{F}$-homology sphere is generically anisotropic over $\mathbb{F}$. In this paper, we prove this conjecture for all strongly edge decomposable spheres. |
| title | The generic anisotropy of strongly edge decomposable spheres |
| topic | Combinatorics Commutative Algebra |
| url | https://arxiv.org/abs/2406.18989 |