Exact values of generic subrank
<|reference_start|>Exact values of generic subrank: 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 $r$.<|reference_end|>
@article{pielasa2024exact,
    title={Exact values of generic subrank},
    author={Pawe{l} Pielasa, Matouv{s} v{S}afr'anek, Anatoli Shatsila},
    journal={arXiv preprint arXiv:2408.07550},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.07550},
    primaryClass={math.AG cs.CC}
}