Alastair Craw ; Liana Heuberger ; Jesus Tapia Amador - Combinatorial Reid's recipe for consistent dimer models

epiga:6085 - Épijournal de Géométrie Algébrique, February 26, 2021, Volume 5 - https://doi.org/10.46298/epiga.2021.volume5.6085
Combinatorial Reid's recipe for consistent dimer models

Authors: Alastair Craw ; Liana Heuberger ; Jesus Tapia Amador

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.


Volume: Volume 5
Published on: February 26, 2021
Submitted on: February 11, 2020
Keywords: Mathematics - Algebraic Geometry,Mathematics - Representation Theory


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