On the central geometry of nonnoetherian dimer algebras

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 $\mathrm{Max}Z$. Furthermore, we show that the reduced center $Z/\mathrm{nil}Z$ is depicted by a Gorenstein singularity, and contains precisely one closed point of positive geometric dimension.

22 pages. This paper is one of four that extends and replaces arXiv:1412.1750