Derived categories of small toric Calabi-Yau 3-folds and counting invariants

Details Derived categories of small toric Calabi-Yau 3-folds and counting invariants Derived categories of small toric Calabi-Yau 3-folds and counting invariants

2008-09-17

arxiv.org/abs/0809.2994v5

Mathematics

Algebraic Geometry

43 pages, 8 figures; section 3.4 revived

Scientific paper

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 systems. As an application we provide certain equations on Donaldson-Thomas, Pandeharipande-Thomas and Szendroi's invariants. Finally, we show that moduli spaces associated with a quiver given by successive mutations are realized as the moduli spaces associated the original quiver by changing the stability conditions.

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