Exact values of generic subrank
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916357231083520 |
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| author | Pielasa, Paweł Šafránek, Matouš Shatsila, Anatoli |
| author_facet | Pielasa, Paweł Šafránek, Matouš Shatsila, Anatoli |
| contents | In this article we prove the subrank of a generic tensor in $\mathbb{C}^{n,n,n}$ to be $Q(n) = \lfloor\sqrt{3n - 2}\rfloor$ by providing a lower bound to the known upper bound. More generally, we find the generic subrank of tensors of all orders and dimensions. This answers two open questions posed in arXiv:2205.15168v2. Finally, we compute dimensions of varieties of tensors of subrank at least $r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact values of generic subrank Pielasa, Paweł Šafránek, Matouš Shatsila, Anatoli Algebraic Geometry Computational Complexity 15A69, 68Q17, 14N07 In this article we prove the subrank of a generic tensor in $\mathbb{C}^{n,n,n}$ to be $Q(n) = \lfloor\sqrt{3n - 2}\rfloor$ by providing a lower bound to the known upper bound. More generally, we find the generic subrank of tensors of all orders and dimensions. This answers two open questions posed in arXiv:2205.15168v2. Finally, we compute dimensions of varieties of tensors of subrank at least $r$. |
| title | Exact values of generic subrank |
| topic | Algebraic Geometry Computational Complexity 15A69, 68Q17, 14N07 |
| url | https://arxiv.org/abs/2408.07550 |