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Non-commutative crepant resolutions

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arxiv math/0211064 v2 pith:KBRX4DFS submitted 2002-11-04 math.RA math.AG

Michel Van den Bergh This is my paper · ORCID
classification math.RAmath.AG
keywords crepantnon-commutativeresolutionssingularitybondalcasescategorycertain
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We introduce the notion of a ``non-commutative crepant'' resolution of a singularity and show that it exists in certain cases. We also give some evidence for an extension of a conjecture by Bondal and Orlov, stating that different crepant resolutions of a Gorenstein singularity have the same derived category.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Geometric helices on del Pezzo surfaces from tilting

    math.AG 2026-03 unverdicted novelty 7.0 of 10

    All geometric helices on del Pezzo surfaces are related by elementary operations including tilting, implying that non-commutative crepant resolutions of their affine cones are related by mutations.

  2. Non-commutative resolutions and pre-quotients of Calabi-Yau double covers

    hep-th 2025-07 conditional novelty 7.0 of 10

    A-periods of non-commutative resolutions of Calabi-Yau double covers satisfy the same GKZ system as those of an explicitly constructed smooth complete intersection.

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