MOS

Abstract

Given a finite subgroup G of SL_n(C) the McKay correspondence studies the relation between G-equivalent geometry of C^n and the geometry of a resolution of Y of C^n/G. In their groundbreaking work, Bridgeland, Kind, and Reid have established that for n = 2,3 the scheme Y = G-Hilb(C^n) is a crepant resolution of C^n/G and that the derived category D(Y) is equivalent to the G-equivalent derived category D^G(C^n). It follows that we also have D(Y) = D^G(C^3) for any other crepant resolution Y of C^3/G. In this talk, I discuss possible ways of generalizing this to dimension 4 and above.