Non-commutative crepant resolutions and their DT invariants

本项目的目的是详细研究与膜平铺（环面上的二部图）相关的环面Calabi-Yau三倍的非交换渐变分辨率。这些褶皱的分辨率是由膜平铺决定的典型的颤势代数。我们将研究它们的Donaldson-Thomas型不变量及其与creent决议的Donaldson-Thomas不变量的关系。我们将研究这个颤振势代数的突变是否可以再次表示为与某些膜平铺相关联的颤振势代数。我们将研究颤势代数的派生范畴中的例外集合。

The purpose of this project is a detailed investigation of the non-commutative crepant resolutions of the toric Calabi-Yau threefolds associated to the brane tilings (bipartite graphs on a torus). These crepant resolutions are quiver potential algebras canonically determined by the brane tiling. We will investigate their Donaldson-Thomas type invariants and their relation to the Donaldson-Thomas invariants of the crepant resolutions. We will investigate if the mutations of this quiver potential algebra can be again represented as quiver potential algebras associated to some brane tilings. We will study exceptional collections in the derived category of the quiver potential algebra.