Counting invariants for the ADE McKay quivers
Counting invariants for the ADE McKay quivers
复制标题
计算 ADE McKay 箭袋的不变量
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Yunfeng Jiang
中科院分区：
文献类型：
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作者：
A. Gholampour;Yunfeng Jiang
我们考虑二元多面体群G < SU（2）< SU（3）的McKay表示的模空间。这种表示的导出范畴等价于在相应的ADE分解Y=G-Hilb（C^3）上的相干层的导出范畴。根据Nagao和Nakajima的思想，通过对上述等价导出范畴的稳定性条件空间中的参数进行特定的选择，我们恢复了Donaldson-Thomas（DT）、Pandharipande-Thomas（PT）和Szendroi（NCDT）模空间。我们还直接计算了Y的Gromov-Witten（GW）配分函数，并将结果表示为相关ADE Dynkin图的根系。然后，我们通过假设DT/PT对应关系来验证GW/DT/NCDT对应关系。Szendroi不变量与Bryan定义的C^3/G的轨道Donaldson-Thomas不变量相同。这将使我们能够验证在这种情况下的轨道Donaldson-Thomas理论的Crepant归结猜想。
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.
影响因子：
3.1
作者：
Pandharipande, R.;Thomas, R. P.
通讯作者：
Thomas, R. P.