Combinatorial Reid's recipe for consistent dimer models

Alastair Craw, Liana Heuberger, Jesus Tapia Amador

Research output: Contribution to journalArticle


Reid's recipe for a finite abelian subgroup G in SL(3,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-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-V\'{e}lez. Our main tool generalises the jigsaw transformations of Nakamura to consistent dimer models.
Original languageEnglish
Number of pages26
Publication statusPublished - 2020

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