Non-Commutative Crepant Resolutions: Scenes from Categorical Geometry
Non-Commutative Crepant Resolutions: Scenes from Categorical Geometry
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DOI：
10.1515/9783110250404.293
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发表时间：
2011-03
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通讯作者：
Graham J. Leuschke
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作者：
Graham J. Leuschke
非交换初等归结是Van den Bergh定义的代数对象，用于实现双曲面几何中派生范畴的等价性。它们是由倾斜理论、McKay对应和最小模型程序驱动的，并在弦论和表示论中有应用。在这篇说明性文章中，我将范登伯格的定义置于这些背景下，并描述了该领域目前的一些研究。
Non-commutative crepant resolutions are algebraic objects defined by Van den Bergh to realize an equivalence of derived categories in birational geometry. They are motivated by tilting theory, the McKay correspondence, and the minimal model program, and have applications to string theory and representation theory. In this expository article I situate Van den Bergh's definition within these contexts and describe some of the current research in the area.