English

Exact values of generic subrank

Algebraic Geometry 2024-08-15 v1 Computational Complexity

Abstract

In this article we prove the subrank of a generic tensor in Cn,n,n\mathbb{C}^{n,n,n} to be Q(n)=3n2Q(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 rr.

Keywords

Cite

@article{arxiv.2408.07550,
  title  = {Exact values of generic subrank},
  author = {Paweł Pielasa and Matouš Šafránek and Anatoli Shatsila},
  journal= {arXiv preprint arXiv:2408.07550},
  year   = {2024}
}

Comments

14 pages, comments welcome!

R2 v1 2026-06-28T18:12:52.510Z