TY - JOUR
T1 - Non-commutative desingularization of determinantal varieties I
AU - Buchweitz, Ragnar Olaf
AU - Leuschke, Graham J.
AU - van den Bergh, Michel
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
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.
UR - http://www.scopus.com/inward/record.url?scp=77955304031&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77955304031&partnerID=8YFLogxK
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 -