Non-commutative desingularization of determinantal varieties I

作者：Buchweitz Ragnar Olaf; Leuschke Graham J^*; Van den Bergh Michel

来源：Inventiones Mathematicae, 2010, 182(1): 47-115.

DOI：10.1007/s00222-010-0258-7

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.

• 出版日期2010-11