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

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 نشر من قبل Kentaro Nagao
 تاريخ النشر 2011
  مجال البحث
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 تأليف Kentaro Nagao




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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 Szendrois 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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