ALGEBRAIC COMBINATORICS

no. 2
Semi-steady non-commutative crepant resolutions via regular dimer models
Nakajima, Yusuke1
1 Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
Algebraic Combinatorics, Volume 2 (2019) no. 2, pp. 173-195.

A consistent dimer model gives a non-commutative crepant resolution (= NCCR) of a 3-dimensional Gorenstein toric singularity. In particular, it is known that a consistent dimer model gives a class of NCCRs called steady if and only if it is homotopy equivalent to a regular hexagonal dimer model. Inspired by this result, we detect another nice property on NCCRs that characterizes square dimer models. We call such NCCRs semi-steady NCCRs, and study their properties.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.39
Classification: 13C14, 05B45, 14E15, 16S38
Keywords: Non-commutative crepant resolutions, Dimer models, Regular tilings, Toric singularities
Nakajima, Yusuke 1

1 Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Nakajima, Yusuke. Semi-steady non-commutative crepant resolutions via regular dimer models. Algebraic Combinatorics, Volume 2 (2019) no. 2, pp. 173-195. doi : 10.5802/alco.39. https://alco.centre-mersenne.org/articles/10.5802/alco.39/

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