Mathematics – Algebraic Geometry
Scientific paper
2009-10-29
Mathematics
Algebraic Geometry
Scientific paper
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.
Gholampour Amin
Jiang Yunfeng
No associations
LandOfFree
Counting invariants for the ADE McKay quivers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Counting invariants for the ADE McKay quivers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counting invariants for the ADE McKay quivers will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-404383