BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

Hilbert Functions of Fat Point Schemes Nagel, Uwe


Information on the Hilbert function of a finite set of fat points is relevant in a variety of studies such as interpolation, linear systems of rational varieties, or the weak Lefschetz property. In particular, one is interested in the least degree from which on the Hilbert function is predictable or, equivalently, its Castelnuovo-Mumford regularity. An optimal upper bound, named after Segre, was conjectured by Trung and, independently, by Fatabbi and Lorenzini in 2001. In joint work with Bill Trok, we recently established this conjecture. Furthermore, we derive an alternate regularity bound that improves the Segre bound in some cases, for example, if the support contains a subset of general points. Among the arguments is a new partition result for matroids.

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International