Exact values of generic subrank

Abstract

In this article we prove the subrank of a generic tensor in $C^{n,n,n}$ to be $Q\left(n\right)=\lfloor \sqrt{3n-2}\rfloor$ 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 [5]. Finally, we compute dimensions of varieties of tensors of subrank at least r.