摘要翻译：
给出了一个具有超势定义关系的颤振代数a，定义了计数框架循环a-模的一组不变量，类似于Calabi-Yau三元数的秩-1 Donaldson-Thomas不变量。对于A为三重普通二重点的非交换裂缝分辨率的特殊情况，利用环面局部化方法证明了在固定边界条件的正方形二聚体模型中，不变量可计算某些金字塔状的分块构型或等价的无穷多个二聚体构型。结果得到的配分函数具有无限乘积展开，它分解为奇点及其flop的交换crepant分解的rank-1级Donaldson-Thomas配分函数。将不同的配分函数推测地解释为在不同的稳定性条件下计算导出的A-模范畴中的稳定对象；它们的关系应该是在这个三角范畴上的稳定条件空间中的墙交叉的一个实例。
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英文标题：
《Non-commutative Donaldson-Thomas theory and the conifold》
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作者：
Balazs Szendroi
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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英文摘要：
  Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A-modules, analogous to rank-1 Donaldson-Thomas invariants of Calabi-Yau threefolds. For the special case when A is the non-commutative crepant resolution of the threefold ordinary double point, it is proved using torus localization that the invariants count certain pyramid-shaped partition-like configurations, or equivalently infinite dimer configurations in the square dimer model with a fixed boundary condition. The resulting partition function admits an infinite product expansion, which factorizes into the rank-1 Donaldson-Thomas partition functions of the commutative crepant resolution of the singularity and its flop. The different partition functions are speculatively interpreted as counting stable objects in the derived category of A-modules under different stability conditions; their relationship should then be an instance of wall crossing in the space of stability conditions on this triangulated category.
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PDF链接：
https://arxiv.org/pdf/0705.3419