Non-commutative desingularization of determinantal varieties, II: Arbitrary minors
Abstract
In our paper "Non-commutative desingularization of determinantal varieties, I" we constructed and studied non-commutative resolutions of determinantal varieties defined by maximal minors. At the end of the introduction we asserted that the results could be generalized to determinantal varieties defined by non-maximal minors, at least in characteristic zero. In this paper we prove the existence of non-commutative resolutions in the general case in a manner which is still characteristic free, and carry out the explicit description by generators and relations in characteristic zero. As an application of our results we prove that there is a fully faithful embedding between the bounded derived categories of the two canonical (commutative) resolutions of a determinantal variety, confirming a well-known conjecture of Bondal and Orlov in this special case.
Keywords
Cite
@article{arxiv.1106.1833,
title = {Non-commutative desingularization of determinantal varieties, II: Arbitrary minors},
author = {Ragnar-Olaf Buchweitz and Graham J. Leuschke and Michel Van den Bergh},
journal= {arXiv preprint arXiv:1106.1833},
year = {2013}
}
Comments
61 pages, greatly expanded. Now includes a complete treatment of the case of characteristic zero. All comments welcome