Claudiu Raicu

ABSTRACT

The Weak Lefschetz Property asks whether multiplication by a general linear form has maximal rank in every degree of a graded Artinian algebra. For monomial complete intersections, this property always holds over fields of characteristic zero. In positive characteristic, however, the Weak Lefschetz Property may fail, and its validity depends on delicate arithmetic interactions between the characteristic of the field and the degrees of the monomial generators. In this talk, I will explain how to obtain a complete numerical characterization of the Weak Lefschetz Property by exploiting its close relationship with the cohomology of line bundles on the incidence correspondence - the partial flag variety parametrizing pairs consisting of a point in projective space and a hyperplane containing it.

Joint work with Annet Kyomuhangi, Emanuela Marangone, and Ethan Reed.