论文标题
非交通性孤立奇异性的前分辨率
Pre-resolutions of noncommutative isolated singularities
论文作者
论文摘要
我们介绍了针对非共同分辨率的正确分辨率（准分辨率）的概念，这是Qin-Wang-Zhang引入的准分辨率的较弱版本。我们证明，在下面有界限的Noetherian的正确分辨率，局部有限的分级代数为2始终是Morita等效的。当我们局限于非交通性二次超曲面时，我们证明了非交易性二次超表面是一种非交易性孤立的奇异性，总是承认正确的前分辨率。此外，我们提供了一种验证非交通性二次超露外表面是否是孤立的奇异性的方法。还包括一个不可或缺的最大Cohen-Macaulay模块和正确分辨率的非共同二次超曲面的示例。
We introduce the notion of right pre-resolutions (quasi-resolutions) for noncommutative isolated singularities, which is a weaker version of quasi-resolutions introduced by Qin-Wang-Zhang. We prove that right quasi-resolutions for noetherian bounded below and locally finite graded algebra with right injective dimension 2 are always Morita equivalent. When we restrict to noncommutative quadric hypersurfaces, we prove that a noncommutative quadric hypersurface, which is a noncommutative isolated singularity, always admits a right pre-resolution. Besides, we provide a method to verify whether a noncommutative quadric hypersurface is an isolated singularity. An example of noncommutative quadric hypersurfaces with detailed computations of indecomposable maximal Cohen-Macaulay modules and right pre-resolutions is included as well.
