Waring decompositions of special binomials

Luca Chiantini, Fulvio Gesmundo, Sara Marziali

We determine the Waring rank of homogeneous polynomials of the form $x^k{y}^k{z}^k+{\ell }^{3k}$ where $\ell$ is a linear form. The result is based on the study of the Hilbert function…