2011/06/09 by Ragnar-Olaf Buchweitz, Buchweitz, Ragnar-Olaf, Graham J. Leuschke +3 · 1 citation
Mathematics · #13C14 #14A22 #14E15 #14M12 #14M15 #15A75 #16S38 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13C14 #msc:14A22 #msc:14E15 #msc:14M12 #msc:14M15 #msc:15A75 #msc:16S38
paper · pdf · doi:10.48550/arxiv.1106.1833
61 pages, greatly expanded. Now includes a complete treatment of the case of characteristic zero. All comments welcome
arxiv created 2013/10/01 · arxiv updated 2013/10/02
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.