GASC Seminar "Jordan type and Lefschetz properties" by Pedro Macias Marques (University of Évora)

Abstract: There has been much interest recently in weak and strong Lefschetz properties of graded Artinian algebras, mainly from the commutative algebra point of view, but also from algebraic geometry problems. We study Artinian Gorenstein (AG) algebras and consider a more general invariant, the set of Jordan types of elements of the maximal ideal, i.e. the partition giving the Jordan blocks of the respective multiplication map.  In a joint work with Chris McDaniel and Tony Iarrobino, we study the generic Jordan type of a free extension of two rings, and of the associated graded algebra of an AG algebra determined by an non-standard-graded AG algebra.