English
Combinatorial Reid's recipe for consistent dimer models
Multi angle
Auteurs : Heuberger, Liana (Auteur de la Conférence)
CIRM (Editeur )
14M25 - Toric varieties, Newton polyhedra
16G20 - Representations of quivers and partially ordered sets
16E35 - Derived categories in associative algebra
14E16 - McKay correspondence
CIRM (Editeur )
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Résumé :
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
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 15/12/2022 Date de captation : 29/11/2022 Sous collection : Research talks arXiv category : Algebraic Geometry Domaine : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 00:38:38 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-29-11_Heuberger.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Algebraic Geometry and Complex Geometry / Géométrie Algébrique et Géométrie ComplexeOrganisateurs de la rencontre : Darondeau, Lionel ; Floris, Enrica Dates : 28/11/2022 - 02/12/2022 Année de la rencontre : 2022 URL Congrès : https://conferences.cirm-math.fr/2605.html
Données de citation
DOI : 10.24350/CIRM.V.19983603Citer cette vidéo: Heuberger, Liana (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 |
Voir aussi
- [Multi angle] Hodge conjecture for singular varieties / Auteur de la Conférence Kaur, Inder.
- [Multi angle] Positivity of higher exterior powers of the tangent bundle / Auteur de la Conférence Gachet, Cécile.
- [Multi angle] Asymptotic behaviour of rational curves / Auteur de la Conférence Faisant, Loïs.
Bibliographie
- 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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