Non-commutative desingularization of determinantal varieties I

By R. Buchweitz, Graham J. Leuschke, Michel van den Bergh. 2009

51 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8d7d72a968b6d97b62269ac18771332f460059a5