Counting invariants for the ADE McKay quivers
arXiv:0910.5551
Abstract
We consider the moduli space of the McKay quiver representations associated to the binary polyhedral groups G < SU(2) < SU(3). The derived category of such representations is equivalent to the derived category of coherent sheaves on the corresponding ADE resolution Y=G-Hilb(C^3). Following the ideas of Nagao and Nakajima, by making particular choices of parameters in the space of stability conditions on the equivalent derived categories above, we recover Donaldson-Thomas (DT), Pandharipande-Thomas (PT) and Szendroi (NCDT) moduli spaces. We also compute the Gromov-Witten (GW) partition function of Y directly and express the result in terms of the root system of the associated ADE Dynkin diagram. We then verify the conjectural GW/DT/NCDT-correspondence by assuming the DT/PT-correspondence. The Szendroi invariants are the same as the orbifold Donaldson-Thomas invariants for C^3/G defined by Bryan. This will allow us to verify the Crepant Resolution Conjecture for the orbifold Donaldson-Thomas theory in this case.
References in corpus (7)
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- Calabi-Yau algebras
- Curve counting via stable pairs in the derived category
- Derived categories of small toric Calabi-Yau 3-folds and counting invariants
- Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
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Cited by in corpus (10)
- Motivic Donaldson-Thomas invariants and McKay correspondence
- Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
- On higher rank Donaldson-Thomas invariants
- Multiple cover formula of generalized DT invariants II: Jacobian localizations
- Crystal Melting, BPS Quivers and Plethystics
- Wall-crossing formulas for framed objects
- Matrix models and stochastic growth in Donaldson-Thomas theory
- Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
- Attractor invariants, brane tilings and crystals
- Behrend's function is constant on Hilb^n(C^3)