# Critical varieties in the Grassmannian

@inproceedings{Galashin2021CriticalVI, title={Critical varieties in the Grassmannian}, author={Pavel Galashin}, year={2021} }

We introduce a family of spaces called critical varieties. Each critical variety is a subset of one of the positroid varieties in the Grassmannian. The combinatorics of positroid varieties is captured by the dimer model on a planar bipartite graph G, and the critical variety is obtained by restricting to Kenyon’s critical dimer model associated to a family of isoradial embeddings of G. This model is invariant under square/spider moves on G, and we give an explicit boundary measurement formula…

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