Exact values of generic subrank
| Autor: | Pielasa, Paweł, Šafránek, Matouš, Shatsila, Anatoli |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $r$. Comment: 14 pages, comments welcome! |
| Databáze: | arXiv |
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