Decompositions and Terracini loci of cubic forms of low rank
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916401634082816 |
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| author | Chiantini, Luca Gesmundo, Fulvio |
| author_facet | Chiantini, Luca Gesmundo, Fulvio |
| contents | We study Waring rank decompositions for cubic forms of rank $n+2$ in $n+1$ variables. In this setting, we prove that if a concise form has more than one non-redundant decomposition of length $n+2$, then all such decompositions share at least $n-3$ elements, and the remaining elements lie in a special configuration. Following this result, we give a detailed description of the $(n+2)$-th Terracini locus of the third Veronese embedding of $n$-dimensional projective space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03715 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Decompositions and Terracini loci of cubic forms of low rank Chiantini, Luca Gesmundo, Fulvio Algebraic Geometry 14N07, 14N05, 15A69 We study Waring rank decompositions for cubic forms of rank $n+2$ in $n+1$ variables. In this setting, we prove that if a concise form has more than one non-redundant decomposition of length $n+2$, then all such decompositions share at least $n-3$ elements, and the remaining elements lie in a special configuration. Following this result, we give a detailed description of the $(n+2)$-th Terracini locus of the third Veronese embedding of $n$-dimensional projective space. |
| title | Decompositions and Terracini loci of cubic forms of low rank |
| topic | Algebraic Geometry 14N07, 14N05, 15A69 |
| url | https://arxiv.org/abs/2302.03715 |