be a trilinear form in R, and let JA denote the ideal of R generated by all the partial derivatives of A. A question that arises from the theory of hyperdeterminants (see [GKZ, page 445]) is the following: What can be said about the ideal JA? A reason for this question emerges, among other things, from results which show that information on the depth of JA and, more finely, on the primary decom...