Decomposition loci of tensors
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914887215611904 |
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| author | Bernardi, Alessandra Oneto, Alessandro Santarsiero, Pierpaola |
| author_facet | Bernardi, Alessandra Oneto, Alessandro Santarsiero, Pierpaola |
| contents | The decomposition locus of a tensor is the set of rank-one tensors appearing in a minimal tensor-rank decomposition of the tensor. For tensors lying on the tangential variety of any Segre variety, but not on the variety itself, we show that the decomposition locus consists of all rank-one tensors except the tangency point only. We also explicitly compute decomposition loci of all tensors belonging to tensor spaces with finitely many orbits with respect to the action of product of general linear groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decomposition loci of tensors Bernardi, Alessandra Oneto, Alessandro Santarsiero, Pierpaola Algebraic Geometry 15A69, 14N07, 14N05 The decomposition locus of a tensor is the set of rank-one tensors appearing in a minimal tensor-rank decomposition of the tensor. For tensors lying on the tangential variety of any Segre variety, but not on the variety itself, we show that the decomposition locus consists of all rank-one tensors except the tangency point only. We also explicitly compute decomposition loci of all tensors belonging to tensor spaces with finitely many orbits with respect to the action of product of general linear groups. |
| title | Decomposition loci of tensors |
| topic | Algebraic Geometry 15A69, 14N07, 14N05 |
| url | https://arxiv.org/abs/2407.18138 |