Non-commutative desingularization of determinantal varieties, I

Details Non-commutative desingularization of determinantal varieties, I Non-commutative desingularization of determinantal varieties, I

2009-11-13

arxiv.org/abs/0911.2659v2

Mathematics

Commutative Algebra

52 pages, 3 figures, all comments welcome

Scientific paper

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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