On steady non-commutative crepant resolutions

Abstract

We introduce special classes of non-commutative crepant resolutions (= NCCR) which we call steady and splitting. We show that a singularity has a steady splitting NCCR if and only if it is a quotient singularity by a finite abelian group. We apply our results to toric singularities and dimer models.

10 pages, to appear in J. Noncommut. Geom., v3: improved the readability of the proof of our main theorem, v2: updated the references

References in corpus (2)

• Flops and Clusters in the Homological Minimal Model Program
• Gorenstein modifications and $\mathbb{Q}$-Gorenstein rings

Cited by in corpus (3)

• Gorenstein modifications and $\mathbb{Q}$-Gorenstein rings
• Remarks on divisorial ideals arising from dimer models
• Cyclic contractions of dimer algebras always exist