Non-commutative desingularization of determinantal varieties I

Ragnar Olaf Buchweitz; Graham J. Leuschke; Michel van den Bergh

doi:10.1007/s00222-010-0258-7

Non-commutative desingularization of determinantal varieties I

Ragnar Olaf Buchweitz, Graham J. Leuschke, Michel van den Bergh

Department of Mathematics

Research output: Contribution to journal › Article

16 Scopus citations

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.

Original language	English (US)
Pages (from-to)	47-115
Number of pages	69
Journal	Inventiones Mathematicae
Volume	182
Issue number	1
DOIs	https://doi.org/10.1007/s00222-010-0258-7
State	Published - 2010

ASJC Scopus subject areas

Mathematics(all)

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Buchweitz, R. O., Leuschke, G. J., & van den Bergh, M. (2010). Non-commutative desingularization of determinantal varieties I. Inventiones Mathematicae, 182(1), 47-115. https://doi.org/10.1007/s00222-010-0258-7

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