Noncommutative resolutions and rational singularities

2006/12/01 by J. T. Stafford, Michel Van den Bergh, Stafford, J. T. +1 · 3 citations
Mathematics · #14A22 #14E15 #16S38 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0612032

openalex publication_date 2006/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be an algebraically closed field of characteristic zero. We show that the centre of a homologically homogeneous, finitely generated k-algebra has rational singularities. In particular if a finitely generated normal commutative k-algebra has a noncommutative crepant resolution, as introduced by the second author, then it has rational singularities.

Citations

• McKay equivalence for symplectic resolutions of singularities

Cited by

• Dimer models and Calabi-Yau algebras
• Non-commutative resolutions of quotient singularities
• Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras

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