scholarly journals Semi-steady non-commutative crepant resolutions via regular dimer models

2019 ◽  
Vol 2 (2) ◽  
pp. 173-195
Author(s):  
Yusuke Nakajima
Keyword(s):  
Crepant Resolutions ◽  
Dimer Models

scholarly journals CONSISTENCY CONDITIONS FOR DIMER MODELS

2012 ◽  
Vol 54 (2) ◽  
pp. 429-447 ◽  
Author(s):  
RAF BOCKLANDT
Keyword(s):  
Crepant Resolution ◽  
Dimer Model ◽  
Consistency Conditions ◽  
Crepant Resolutions ◽  
Dimer Models

AbstractDimer models are a combinatorial tool to describe certain algebras that appear as noncommutative crepant resolutions of toric Gorenstein singularities. Unfortunately, not every dimer model gives rise to a noncommutative crepant resolution. Several notions of consistency have been introduced to deal with this problem. In this paper, we study the major different notions in detail and show that for dimer models on a torus, they are all equivalent.

scholarly journals Dimer models and crepant resolutions

2016 ◽  
Vol 45 (1) ◽  
pp. 1-42 ◽  
Author(s):  
Akira ISHII ◽  
Kazushi UEDA
Keyword(s):  
Crepant Resolutions ◽  
Dimer Models

scholarly journals Folding of Hitchin Systems and Crepant Resolutions

2021 ◽  
Author(s):  
Florian Beck ◽  
Ron Donagi ◽  
Katrin Wendland
Keyword(s):  
Fixed Point ◽  
Lie Algebras ◽  
Integrable Systems ◽  
Trace Back ◽  
Dynkin Diagrams ◽  
Or Groups ◽  
Hitchin Systems ◽  
Singular Fibers ◽  
Crepant Resolutions ◽  
Intermediate Jacobian

Abstract Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of $\textrm{ABCDEFG}$-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of $\textrm{ADE}$-type. In this article, we implement the techniques of folding by graph automorphisms for Hitchin integrable systems. We show that the fixed point loci of these automorphisms are isomorphic as algebraic integrable systems to the Hitchin systems of the folded groups away from singular fibers. The latter Hitchin systems are isomorphic to the intermediate Jacobian fibrations of Calabi–Yau orbifold stacks constructed by the 1st author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi–Yau three-folds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems.

scholarly journals Coulomb and Liquid Dimer Models in Three Dimensions

2003 ◽  
Vol 91 (16) ◽  
Author(s):  
David A. Huse ◽  
Werner Krauth ◽  
R. Moessner ◽  
S. L. Sondhi
Keyword(s):  
Three Dimensions ◽  
Dimer Models

scholarly journals Non-commutative crepant resolutions for some toric singularities. II

2020 ◽  
Vol 14 (1) ◽  
pp. 73-103
Author(s):  
Špela Špenko ◽  
Michel Van den Bergh
Keyword(s):  
Crepant Resolutions
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