English

Non-commutative desingularization of determinantal varieties, I

Commutative Algebra 2015-05-14 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.0911.2659,
  title  = {Non-commutative desingularization of determinantal varieties, I},
  author = {Ragnar-Olaf Buchweitz and Graham J. Leuschke and Michel Van den Bergh},
  journal= {arXiv preprint arXiv:0911.2659},
  year   = {2015}
}

Comments

52 pages, 3 figures, all comments welcome