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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2508.16796 |
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| _version_ | 1866912551205339136 |
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| author | Bezerra, Lenin Ferrer, Viviana Gondim, Rodrigo |
| author_facet | Bezerra, Lenin Ferrer, Viviana Gondim, Rodrigo |
| contents | We study two special families of cubic hypersurfaces with vanishing Hessian in $\mathbb{P}^N$, obtaining rational parametrizations and computing their degree in $\mathbb{P}(S_3)$. For $N \leq 6$, these two families exhaust the locus of cubics with vanishing Hessian that are not cones. As a consequence, via Macaulay-Matlis duality, we obtain a description of the locus in $\mathrm{Gor}(1, n, n, 1)$ corresponding to those algebras that satisfy the Strong Lefschetz property, for $n \leq 7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Lefschetz locus in Gor(1,n,n,1) Bezerra, Lenin Ferrer, Viviana Gondim, Rodrigo Algebraic Geometry We study two special families of cubic hypersurfaces with vanishing Hessian in $\mathbb{P}^N$, obtaining rational parametrizations and computing their degree in $\mathbb{P}(S_3)$. For $N \leq 6$, these two families exhaust the locus of cubics with vanishing Hessian that are not cones. As a consequence, via Macaulay-Matlis duality, we obtain a description of the locus in $\mathrm{Gor}(1, n, n, 1)$ corresponding to those algebras that satisfy the Strong Lefschetz property, for $n \leq 7$. |
| title | On the Lefschetz locus in Gor(1,n,n,1) |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.16796 |