Lisa Nicklasson: Perazzo algebras and their Hilbert functions

Abstract.

A Perazzo form is a type of homogeneous polynomial whose Hessian determinant is identically zero. As a consequence, an Artinian Gorenstein algebra defined by a Perazzo form (a Perazzo algebra) never has the strong Lefschetz property. In this talk I will summarize recent results and open problems about Hilbert functions and the weak Lefschetz property of Perazzo algebras.