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On the central geometry of nonnoetherian dimer algebras
Journal of Pure and Applied Algebra ( IF 0.8 ) Pub Date : 2021-08-01 , DOI: 10.1016/j.jpaa.2020.106590
Charlie Beil

Let $Z$ be the center of a nonnoetherian dimer algebra on a torus. Although $Z$ itself is also nonnoetherian, we show that it has Krull dimension $3$, and is locally noetherian on an open dense set of $\operatorname{Max}Z$. Furthermore, we show that the reduced center $Z/\operatorname{nil}Z$ is depicted by a Gorenstein singularity, and contains precisely one closed point of positive geometric dimension.

中文翻译:

关于非诺特二聚体代数的中心几何

设 $Z$ 是环面上的非诺以太二聚体代数的中心。虽然$Z$ 本身也是非noetherian,但我们证明它具有Krull 维$3$,并且在$\operatorname{Max}Z$ 的开稠密集上是局部noetherian。此外,我们表明缩小的中心 $Z/\operatorname{nil}Z$ 由 Gorenstein 奇点描述,并且恰好包含一个正几何维度的闭合点。
更新日期:2021-08-01
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