Title: Waring loci and decompositions of low rank symmetric tensors
Abstract: Given a symmetric tensor, i.e., a homogeneous polynomial, a
Waring decomposition is a decomposition as sum of symmetric
decomposable tensors, i.e., powers of linear forms. We call Waring
rank of a homogenous polynomial the smallest length of such a Waring
decomposition. In this talk, I want to introduce the concept of Waring
locus of a homogeneous polynomial, i.e., the locus of linear forms
which may appear in a minimal Waring decomposition. Then, after showing
some example on how Waring loci can be computed in specific cases, I
explain how they may be used to construct minimal Waring decompositions.
These results are from recent joint works with E. Carlini, M.V.
Catalisano, and B. Mourrain.