Derived categories of small toric Calabi-Yau 3-folds and counting invariants
Derived categories of small toric Calabi-Yau 3-folds and counting invariants
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DOI：
10.1093/qmath/har025
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发表时间：
2008-09
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影响因子：
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通讯作者：
K. Nagao
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文献类型：
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作者：
K. Nagao
我们首先构造了3重仿射环状Calabi-Yau箭图的小阶解与具有超势的箭图之间的一个导出等价。在此等价性下，我们建立了反转相干系统计数不变量母函数的穿越公式。作为应用，我们给出了关于Donaldson-Thomas、Pandeharipande-Thomas和Szendroi不变量的某些方程。最后，我们证明了通过改变稳定性条件，与由连续突变给出的箭图相关的模空间被实现为与原箭图相关的模空间。
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.