ALGEBRAIC COMBINATORICS

no. 2

Semi-steady non-commutative crepant resolutions via regular dimer models
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: 2017-08-17
Revised: 2018-06-05
Accepted: 2018-08-06
Published online: 2019-03-05
DOI: https://doi.org/10.5802/alco.39
Classification: 13C14,  05B45,  14E15,  16S38
Keywords: Non-commutative crepant resolutions, Dimer models, Regular tilings, Toric singularities 
@article{ALCO_2019__2_2_173_0,
     author = {Nakajima, Yusuke},
     title = {Semi-steady non-commutative crepant resolutions via regular dimer models},
     journal = {Algebraic Combinatorics},
     pages = {173--195},
     publisher = {MathOA foundation},
     volume = {2},
     number = {2},
     year = {2019},
     doi = {10.5802/alco.39},
     mrnumber = {3934827},
     zbl = {1419.13019},
     language = {en},
     url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_2_173_0/}
}
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/item/ALCO_2019__2_2_173_0/

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