English

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 33-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.

Keywords

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

R2 v1 2026-06-22T15:22:58.410Z