On apolarity and generic canonical forms

The notion of S-algebra is introduced. The theory of apolarity and generic canonical forms for polynomials is generalized to S-algebras over the compl ex field C. We apply this theory to the problem of finding the essential ra nk of general, symmetric, and skew-symmetric tensors. Upper bounds for the essential ranks are found by different combinatorial coverings. (C) 1999 Ac ademic Press.