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

Source: arXiv

ABSTRACT 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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