A consistent dimer model gives a non-commutative crepant resolution (= NCCR) of a -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.
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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