Koszul duality and the McKay correspondence
Chris Brav (Queens University, Ontario)
Monday 7th April, 2008 16:00-17:00 214, Mathematics Building
The McKay correspondence relates the equivariant geometry of a finite group G acting on a variety X to the geometry of the quotient X/G and its resolutions. We consider the case of G acting linearly on a vector space V, give a natural construction of a tilting object in the category of G-sheaves on V, and show that its endomorphism algebra is Koszul. As applications of this construction, we relate the McKay correspondence for P^1 to the classical McKay correspondence for C^2 and give a description of the derived category of coherent sheaves on the Hilbert scheme of points in the plane.