Bek Chase: Almost complete intersections and the strong Lefschetz property

Abstract.

Motivated by the foundational result of Stanley that a monomial complete intersection has the strong Lefschetz property (SLP) in characteristic zero, it is natural to ask when monomial almost complete intersections have the SLP. In this talk, we will investigate the strong Lefschetz property for monomial almost complete intersections, providing a complete classification of the SLP for two classes of such algebras in codimension three. Furthermore, we discuss tensor products of these algebras, proving the SLP holds in some higher codimension cases. Our results are obtained primarily via a study of the Hilbert series of these algebras, in particular a characterization of when they are almost centered or symmetric.

This is based on joint work with Filip Jonsson Kling.