Combinatorial Reid's recipe for consistent dimer models
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866914755512369152 |
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| author | Craw, Alastair Heuberger, Liana Amador, Jesus Tapia |
| author_facet | Craw, Alastair Heuberger, Liana Amador, Jesus Tapia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_07506 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Combinatorial Reid's recipe for consistent dimer models Craw, Alastair Heuberger, Liana Amador, Jesus Tapia Algebraic Geometry Representation Theory 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. |
| title | Combinatorial Reid's recipe for consistent dimer models |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2001.07506 |