# On the central geometry of nonnoetherian dimer algebras

## TL;DR

This paper investigates the geometric properties of the center of nonnoetherian dimer algebras on a torus, revealing its Krull dimension, local noetherianity, and singularity structure.

## Contribution

It demonstrates that the center has Krull dimension 3, is locally noetherian on a dense set, and its reduced center exhibits a Gorenstein singularity with a unique positive-dimensional closed point.

## Key findings

- Center has Krull dimension 3.
- Center is locally noetherian on an open dense set.
- Reduced center has a Gorenstein singularity with one positive-dimensional closed point.

## 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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Source: https://tomesphere.com/paper/1903.10460