Combinatorial Reid's recipe for consistent dimer models
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 obje...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Association Epiga
2021-02-01
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| Series: | Épijournal de Géométrie Algébrique |
| Subjects: | |
| Online Access: | https://epiga.episciences.org/6085/pdf |
| Summary: | 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-V\'{e}lez. Our main tool
generalises the jigsaw transformations of Nakamura to consistent dimer models. |
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| ISSN: | 2491-6765 |