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Combinatorial Reid's recipe for consistent dimer models
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14M25 - Toric varieties, Newton polyhedra
16G20 - Representations of quivers and partially ordered sets
16E35 - Derived categories in associative algebra
14E16 - McKay correspondence
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Abstract :
Reid's recipe is an equivalent of the McKay correspondence in dimension three. It marks interior line segments and lattice points in the fan of the G-Hilbert scheme (a specific crepant resolution of $\mathbb{C}^{3} / G$ for $G \subset S L(3, \mathbb{C})$ ) with characters of irreducible representations of $G$. Our goal is to generalise this by marking the toric fan of a crepant resolution of any affine Gorenstein singularity, in a way that is compatible with both the G-Hilbert case and its categorical counterpart known as Derived Reid's Recipe. To achieve this, we foray into the combinatorial land of quiver moduli spaces and dimer models. This is joint work with Alastair Craw and Jesus Tapia Amador.
Keywords : Reid's recipe; dimer model; quiver moduli space
MSC Codes : Keywords : Reid's recipe; dimer model; quiver moduli space
14M25 - Toric varieties, Newton polyhedra
16G20 - Representations of quivers and partially ordered sets
16E35 - Derived categories in associative algebra
14E16 - McKay correspondence
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Information on the Video
Language : EnglishAvailable date : 15/12/2022 Conference Date : 29/11/2022 Subseries : Research talks arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:38:38 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-29-11_Heuberger.mp4 
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Information on the Event
Event Title : Algebraic Geometry and Complex Geometry 2022 / Géométrie Algébrique et Géométrie Complexe 2022Dates : 28/11/2022 - 02/12/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2605.html
Citation Data
DOI : 10.24350/CIRM.V.19983603Cite this video as: (2022). Combinatorial Reid's recipe for consistent dimer models. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19983603 URI : http://dx.doi.org/10.24350/CIRM.V.19983603 |
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Bibliography
- AMADOR, Jesus Tapia, HEUBERGER, Liana, et CRAW, Alastair. Combinatorial Reid's recipe for consistent dimer models. Épijournal de Géométrie Algébrique, 2021, vol. 5. - https://doi.org/10.46298/epiga.2021.volume5.6085
- ISHII, A. et UEDA, K. On moduli spaces of quiver representations associated with brane tilings Higher dimensional algebraic varieties and vector bundles, 127141, RIMS Kokyuroku Bessatsu, B9. Res. Inst. Math. Sci.(RIMS), Kyoto, 2008. - http://hdl.handle.net/2433/176749
- CRAW, Alastair. An explicit construction of the McKay correspondence for A-Hilb C3. Journal of Algebra, 2005, vol. 285, no 2, p. 682-705. - https://doi.org/10.1016/j.jalgebra.2004.10.001
- BOCKLANDT, Raf, CRAW, Alastair, et QUINTERO VÉLEZ, Alexander. Geometric Reid's recipe for dimer models. Mathematische Annalen, 2015, vol. 361, no 3, p. 689-723. - http://dx.doi.org/10.1007/s00208-014-1085-8
- BOCKLANDT, Raf, CRAW, Alastair, et QUINTERO VÉLEZ, Alexander. Correction to: Geometric Reid's recipe for dimer models. Mathematische Annalen, 2021, vol. 380, no 1, p. 911-913. - http://dx.doi.org/10.1007/s00208-020-02127-w
- CAUTIS, Sabin, CRAW, Alastair, et LOGVINENKO, Timothy. Derived Reid's recipe for abelian subgroups of SL3 (ℂ). Journal für die reine und angewandte Mathematik (Crelles Journal), 2017, vol. 2017, no 727, p. 1-48. - https://doi.org/10.1515/crelle-2014-0086
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