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arXiv · 1903.10460

On the central geometry of nonnoetherian dimer algebras

Charlie Beil
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Abstract

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.

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Charlie Beil. 2019-03-25. On the central geometry of nonnoetherian dimer algebras. https://arxiv.org/abs/1903.10460

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