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

Authors
  • Nagao, Kentaro
Type
Preprint
Publication Date
Feb 06, 2011
Submission Date
Sep 17, 2008
Source
arXiv
License
Yellow
External links

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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