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.
Buchweitz, Ragnar-Olaf; Leuschke, Graham J.; and Van Den Bergh, Michel, "Non-Commutative Desingularization of Determinantal Varieties, I" (2009). Mathematics Faculty Scholarship. 37.
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