Using the theory of dimer models Broomhead proved that every 3-dimensional Gorenstein affine toric variety Spec $R$ admits a toric non-commutative crepant resolution (NCCR). We give an alternative proof of this result by constructing a tilting bundle on a (stacky) crepant resolution of Spec $R$ using standard toric methods. Our proof does not use dimer models.

中文翻译：

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某些复曲面奇点的非可交换新近分辨率。II

使用二聚体模型理论，Broomhead证明了每3维Gorenstein仿射复曲面Spec $ R $都承认复曲面非交换的新近分解（NCCR）。我们通过使用标准复曲面方法以Spec $ R $的（堆叠）新近分辨率构造倾斜束来提供此结果的替代证明。我们的证明不使用二聚体模型。