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arXiv · 0911.2659

Non-commutative desingularization of determinantal varieties, I

Ragnar-Olaf Buchweitz·Graham J. Leuschke·Michel Van den Bergh
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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.

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Ragnar-Olaf Buchweitz, Graham J. Leuschke, Michel Van den Bergh. 2009-11-14. Non-commutative desingularization of determinantal varieties, I. https://doi.org/10.1007/s00222-010-0258-7

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