A combinatorial proof of the smoothness of catalecticant schemes associated to complete intersections (Q1684292)

\textit{A. Iarrobino} and \textit{V. Kanev} introduced in [Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman. Berlin: Springer (1999; Zbl 0942.14026)] the catalecticant varieties and schemes in relation to the problem of representing a homogeneous form as a sum of powers of linear forms as well as related questions. Of special interest are the irreducible components and smoothness properties of such schemes. For zero-dimensional complete intersections with homogeneous ideal generators of equal degrees over an algebraically closed field of characteristic zero, the author gives a combinatorial proof of the smoothness of the corresponding catalecticant schemes along an open subset of a particular irreducible component.