Non-commutative desingularization of determinantal varieties, I

Abstract

We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.

52 pages, 3 figures, all comments welcome

References in corpus (2)

• Non-commutative Donaldson-Thomas theory and the conifold
• Noncommutative Counterparts of the Springer Resolution

Cited by in corpus (14)

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• Non-commutative desingularization of determinantal varieties, II: Arbitrary minors
• Categorical Plücker Formula and Homological Projective Duality
• Noncommutative desingularization of orbit closures for some representations of $G{L}_n$
• Derived categories of Quot schemes of locally free quotients
• Gorenstein modifications and $\mathbb{Q}$-Gorenstein rings
• The Cohomology Annihilator of a Curve Singularity
• On steady non-commutative crepant resolutions
• Homological Projective Duality for Determinantal Varieties
• Noncommutative (crepant) desingularizations and the global spectrum of commutative rings
• Non-commutative crepant resolution of minimal nilpotent orbit closures of type A and Mukai flops
• On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions
• Semi-steady non-commutative crepant resolutions via regular dimer models
• On Cohomology of Complexes Associated with a Generic Matrix