Roy Skjelnes: Classification and geometry of smooth Hilbert schemes

Abstract

The aim of the talk is discuss a classification of smooth Hilbert schemes. We have the Hilbert scheme parametrizing subschemes of a fixed projective m-space, having a fixed Hilbert polynomial. Each Hilbert polynomial is described by an integer partition, and the classification result describes numerical conditions on the partitions. Moreover, the result yields a description of the geometry of the smooth Hilbert schemes, and a description of the geometry of the objects parametrized.

The talk is a report of a joint work with Greg Smith (Queens University, Canada).