DERIVED CATEGORIES OF SMALl TORIC CALABI-YAU 3-FOLDS AND CURVE COUNTING INVARIANTS

We first construct a derived equivalence between a small crepant resolution of an affine toric Calabi-Yau 3-fold and a certain quiver with a superpotential. Under this derived equivalence, we establish a wall-crossing formula for the generating function of the counting invariants of perverse coherent sheaves. As an application, we provide some equations on Donaldson-Thomas, Pandharipande-Thomas and Szendroi's invariants.