Abstract

The crepant resolution conjecture for Donaldson-Thomas invariants is a conjecture in enumerative geometry originating from string theory. It relates the Donaldson-Thomas generating series of a certain type of threedimensional Calabi-Yau orbifold to that of a particular crepant resolution of its coarse moduli space. We discuss an approach to study this conjecture using derived category methods. As a partial result, we present a wall-crossing formula in (a variant of) Joyce's motivic Hall algebra. Our formula relates the Hilbert scheme of curves on the orbifold to the Hilbert scheme of curves on the resolution.This is a first step towards potentially proving the crepant resolution conjecture for Donaldson-Thomas invariants.