Typical ranks for 3-tensors, nonsingular bilinear maps and determinantal ideals

Toshio Sumi, Mitsuhiro Miyazaki, Toshio Sakata

Let $m,n\ge 3$, $(m-1)(n-1)+2\le p\le mn$, and $u=mn-p$. The set ${\mathbb{R}}^{u\times n\times m}$ of all real tensors with size $u\times n\times m$ is one to one corresponding t…