Waring identifiability for powers of forms via degenerations

Abstract

We discuss an approach to the secant non‐defectivity of the varieties parametrising th powers of forms of degree . It employs a Terracini‐type argument along with certain degeneration arguments, some of which are based on toric geometry. This implies a result on the identifiability of the Waring decompositions of general forms of degree kd as a sum of th powers of degree forms, for which an upper bound on the Waring rank was proposed by Fröberg, Ottaviani and Shapiro.