TY - JOUR
T1 - Non-commutative desingularization of determinantal varieties I
AU - Buchweitz, Ragnar Olaf
AU - Leuschke, Graham J.
AU - van den Bergh, Michel
N1 - Funding Information:
The first author was partly supported by NSERC grant 3-642-114-80. The second author was partly supported by NSA grant H98230-05-1-0032 and NSF grant DMS 0556181. The third author is director of research at the FWO.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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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U2 - 10.1007/s00222-010-0258-7
DO - 10.1007/s00222-010-0258-7
M3 - Article
AN - SCOPUS:77955304031
VL - 182
SP - 47
EP - 115
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
IS - 1
ER -