Description
Abstract: Grothendieck's Quot schemes — moduli spaces of quotient sheaves — are fundamental objects in algebraic geometry, but we know very little about them. This talk will focus on a relatively simple special case: the Quot scheme Quot^l (E) of length l quotients of a vector bundle E of rank r on a smooth surface S. The scheme Quot^l (E) is a cross of the Hilbert scheme of points of S (E = O) and the projectivisation of E (l = 1); it carries a virtual fundamental class, and if l and r are at least 2, then Quot^l (E) is singular. I will explain how the ADHM description of Quot^l (E) provides a conjectural description of the singularities, and show how they can be resolved in the l = 2 case. Furthermore, I will describe the relation between Quot^l (E) and Quot^l of a quotient of E, prove a functoriality result for the virtual fundamental class, and use it to compute certain tautological integrals over Quot^l (E).
For Zoom access please contact Andras Stipsicz (stipsicz.andras[a]renyi.hu).