Combinatorial Reid's recipe for consistent dimer models

Alastair Craw, Liana Heuberger, Jesus Tapia Amador

Research output: Contribution to journalArticlepeer-review


Reid's recipe [Rei97, Cra05] for a finite abelian subgroup G ⊂ 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 [CL09] that describes certain objects in the derived category of G-Hilb in terms of Reid's recipe was later proved by Logvinenko et. al. [Log10, CCL17]. 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 [BCQ15]. Our main tool generalises the jigsaw transformations of Nakamura [Nak01] to consistent dimer models.

Original languageFrench
Article number4
Number of pages29
JournalÉpijournal de Géométrie Algébrique
Early online date26 Feb 2021
Publication statusPublished - 26 Feb 2021


  • Dimer model
  • Jigsaw transformations
  • Quiver moduli space
  • Reid's recipe
  • Tilting bundle

ASJC Scopus subject areas

  • Geometry and Topology
  • Algebra and Number Theory


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