Eric Dannetun: Betti numbers of ideals generated by n+1 powers of general linear forms

Abstract: Recently ideals generated by powers of general linear forms have been studied by many authors from different perspectives, especially in regards to Lefschetz properties and the connection to ideals of fat points. In this talk we will study the Betti numbers of ideals generated by n+1 powers of general linear forms (in n variables). Our main result, generalizing recent work of Diethorn et al. (who considered squares of linear forms), is that we determine the Betti numbers when at least one of the generators is a square. The proof relies on the theory of liftable modules and relating the ideals to a finite set of projective points. As a result we find an interesting structure on the syzyiges of the ideals, and moreover that a generic ideal generated by n+1 forms, where at least one is a quadric, is level. Similarly we describe the Betti numbers of the linked artinian gorenstien algebras, and if time permits we will discuss descriptions of their generators and show that they have the strong Lefshcetz property.