Abstract: An Artinian standard graded algebra A has the weak Lefschetz property if the map induced by multiplication by a general linear form has maximal rank (i.e., is injective or surjective) in each degree, and has the strong Lefschetz property if the map induced by multiplication by every power of a general linear form has maximal rank in each degree. In this talk, we will investigate the strong Lefschetz property for almost complete intersections, providing a complete classification for a class of codimension three monomial almost complete intersections. Furthermore, we prove the SLP in some cases for monomial almost complete intersections in arbitrary codimension. This is joint work with Filip Jonsson Kling.
