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arXiv · 2606.15401

Cohen Macaulay modules and positroid varieties

Liam Riordan
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Abstract

Jensen, King, and Su described a category $\operatorname{CM}(C)$ which categorifies the cluster structure on the homogeneous coordinate ring of a Grassmannian. In this paper we describe subcategories $\operatorname{R}(v,w) \subseteq \operatorname{CM}(C)$ which lift Leclerc's categories $\mathcal{C}_{v,w}$ in the case where $v \in \left(W^{k}\backslash W\right)^{\max}$ and $w \geq v.$ As such, these categories are Frobenius, stably 2-CY, have natural cluster characters, and induce a cluster structure in lifts of open positroid varieties.

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Liam Riordan. 2026-06-13. Cohen Macaulay modules and positroid varieties. https://arxiv.org/abs/2606.15401

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