Non-commutative desingularizations of determinantal varieties

Given a determinantal variety, we construct a maximal Cohen-Macaulay module over it such that the endomorphism ring has finite global dimension.  The endomorphism ring can be considered as a non-commutative version of a resolution of singularities for the variety.  We describe the endomorphism ring explicitly in terms of a quiver with relations.  This is ongoing work with Ragnar-Olaf Buchweitz and Michel Van den Bergh.

Graham J. Leuschke