Geodesic
Combinatorial Reid's recipe for consistent dimer models
Épijournal de Géométrie Algébrique, Tome 5 (2021)

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Reid's recipe for a finite abelian subgroup $G\subset \text{SL}(3,\mathbb{C})$ is a combinatorial procedure that marks the toric fan of the $G$-Hilbert scheme with irreducible representations of $G$. The geometric McKay correspondence conjecture of Cautis–Logvinenko that describes certain objects in the derived category of $G\text{-Hilb}$ in terms of Reid's recipe was later proved by Logvinenko et al. We generalise Reid's recipe to any consistent dimer model by marking the toric fan of a crepant resolution of the vaccuum moduli space in a manner that is compatible with the geometric correspondence of Bocklandt–Craw–Quintero-Vélez. Our main tool generalises the jigsaw transformations of Nakamura to consistent dimer models. 
@article{10_46298_epiga_2021_volume5_6085,
     author = {Craw, Alastair and Heuberger, Liana and Amador, Jesus Tapia},
     title = {Combinatorial {Reid's} recipe for consistent dimer models},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {5},
     year = {2021},
     doi = {10.46298/epiga.2021.volume5.6085},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2021.volume5.6085/}
}
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Craw, Alastair; Heuberger, Liana; Amador, Jesus Tapia. Combinatorial Reid's recipe for consistent dimer models. Épijournal de Géométrie Algébrique, Tome 5 (2021). doi: 10.46298/epiga.2021.volume5.6085

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