On the generic and typical ranks of 3-tensors

We study the generic and typical ranks of 3-tensors of dimension l, m, n using results from matrices and algebraic geometry. We state a conjecture about the exact values of the generic rank of 3-tensors over the complex numbers, which is veried numerically for l; m; ≤ n 14. We also discuss the typical ranks over the real numbers, and give an example of an innite family of 3-tensors of the form l = m; n = (m-1)2 + 1;m = 3; 4,..., which have at least two typical ranks.