Combinatorial Reid's recipe for consistent dimer models

Alastair Craw, Liana Heuberger, Jesus Tapia Amador

Research output: Contribution to journalArticlepeer-review

Abstract

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
Article number4
Number of pages26
JournalÉpijournal de Géométrie Algébrique
Volume5
Early online date26 Feb 2021
Publication statusE-pub ahead of print - 26 Feb 2021

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