Waring identifiability for powers of forms via degenerations

Abstract

We discuss an approach to the secant non-defectivity of the varieties parametrizing $k$-th powers of forms of degree $d$. 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 $k$-th powers of degree $d$ forms, for which an upper bound on the Waring rank was proposed by Fr\"oberg, Ottaviani and Shapiro.