Preresolutions of noncommutative isolated singularities
Preresolutions of noncommutative isolated singularities
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DOI：
10.2140/pjm.2022.316.367
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发表时间：
2020-05
影响因子：
0.6
通讯作者：
Ji-wei He;Yu Ye
中科院分区：
文献类型：
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作者：
Ji-wei He;Yu Ye
本文引入了非对易孤立奇点的右预归结（拟归结）的概念，它是秦王张引入的拟归结的一个较弱的形式。证明了右内射维数为2的Noether下有界分次代数和局部有限分次代数的右拟分解总是Morita等价的。当我们限制到非交换二次超曲面时，我们证明了一个非交换二次超曲面，它是一个非交换孤立奇点，总是允许一个右预分解。此外，我们还提供了一种方法来验证非交换二次超曲面是否是孤立奇点。一个例子的非交换二次超曲面的不可分解的极大Cohen-Macaulay模和右预分解的详细计算也包括在内。
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.