A characterization of degenerate tridimensional tensors

We can estabilish when a tridimensional hypermatrix (tensor) defines a degenerate multilinear form by studying “degenerate points” (singular or “unexpected” points) of some determinantal schemes associated to it. More precisely, we shall prove that a tridimensional hypermatrix is degenerate if and only if the three determinantal schemes associated to it have “degenerate” points.