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 $r$.
Categories: math.AG cs.CC