Non-commutative crepant resolutions and their DT invariants

本项目的目的是详细研究与膜拼接（环面上的二分图）相关的环面Calabi-Yau三重图的非交换crepant分解。这些可分解性是由膜镶嵌正则确定的可分解势代数。我们将研究它们的Donaldson-Thomas类型不变量以及它们与crepant归结的Donaldson-Thomas不变量的关系。我们将研究这个位势代数的突变是否可以再次表示为与某些膜镶嵌相关联的位势代数。我们将研究特殊集合在导出范畴的位势代数。

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.