Mats boij: Waring rank and SLP for annihilators of symmetric forms

Abstract

In a joint work with Migliore, Miró-Roig and Nagel, we study Gorenstein algebras defined by the annihilators of symmetric forms. In particular we obtain a complete picture of what happens for symmetric cubics in terms of the Strong Lefschetz Property (SLP) and the Waring rank. We also prove that complete symmetric forms of any degree give algebras satisfying the SLP and we provide a surprisingly short power sum decomposition for them.