Orateur
Prof.
Rosa Maria Miró-Roig
(Universitat de Barcelona)
Description
It is an extremely elusive problem to determine which standard Artinian Gorenstein graded K-algebras satisfy the weak Lefschetz property (WLP). Codimension 2 Artinian Gorenstein graded K-algebras have the WLP and it is open to what extent such result might work for codimension 3 Artinian Gorenstein graded K-algebras.
In this talk I will summarize what we know about this problem and, in particular, I will show that all Artinian Gorenstein K-algebras of codimension 3 with arbitrary socle degree d, arbitrary Sperner number α and at least three peaks (i.e., three values of the h-vector reaching the Sperner number) do satisfy the WLP.
