行列式簇的非交换去奇异化
Non-commutative desingularization of determinantal varieties, I
摘要：
我们证明了由一般矩阵的极大次子定义的行列式簇具有非交换的去奇异化，即我们在这样一个簇上构造了一个极大Cohen-Macaulay模，其自同态环是Cohen-Macaulay且具有有限的整体维数.在方阵的行列式的情况下，这给出了非交换的crepant解决方案。
英文摘要：
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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