CHIANTINI , Luca

Let f be a homogeneous form of degree d in n variables. A Waring decomposition of f is a way to express f as a sum of dth powers of linear forms. In this paper we consider the decompositions of a form as a sum of expressions, each of which is a fixed monomial evaluated at linear forms.

Let $f$ be a homogeneous form of degree d in n variables. A Waring decomposition of $f$ is a way to express $$f as a sum of $d th$ powers of linear forms. In this paper we consider the decompositions of a form as a sum of expressions, each of which is a fixed monomial evaluated at linear forms.

For any irreducible non-degenerate variety $X \subset \mathbb{P}^r$ , we relate the dimension of the $s$-th secant varieties of the Segre embedding of $\mathbb{P}^k\times X$ to the dimension of the $(k,s)$-Grassmann secant variety $GS_X(k,s)$ of $X$. We also give a criterion for the $s$-identifiability of $X$.