Samuel Stark: Geometry of Quot schemes

Abstract

I will describe some of my recent results on the Quot scheme of length l coherent sheaf quotients of a locally free sheaf E of rank r on a smooth projective scheme S. Introduced by Grothendieck, this moduli scheme is a generalization of the Grassmannian (S a point), the projectivization of E (\(l=1\)), and the Hilbert scheme of l points of S (\(r=1\)). Special emphasis will be put on the intersection theory and the tautological sheaves.