Semi-steady non-commutative crepant resolutions via regular dimer models
Representation Theory
2018-10-02 v3 Commutative Algebra
Combinatorics
Abstract
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 nice class of NCCRs called steady if and only if it is homotopy equivalent to a regular hexagonal dimer model. Inspired by this result, we introduce the notion of semi-steady NCCRs, and show a consistent dimer model gives a semi-steady NCCR if and only if it is homotopy equivalent to a regular dimer model.
Cite
@article{arxiv.1608.05162,
title = {Semi-steady non-commutative crepant resolutions via regular dimer models},
author = {Yusuke Nakajima},
journal= {arXiv preprint arXiv:1608.05162},
year = {2018}
}
Comments
19 pages, to appear in Algebraic Combinatorics, v3: major revisions, especially the proof of Theorem 4.2 has been modified, v2: minor changes