TY - JOUR
T1 - Non-commutative Desingularization of Determinantal Varieties, II
T2 - Arbitrary Minors
AU - Buchweitz, Ragnar Olaf
AU - Leuschke, Graham J.
AU - Van Den Bergh, Michel
N1 - Publisher Copyright:
© 2015 The Author(s). Published by Oxford University Press. All rights reserved.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
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U2 - 10.1093/imrn/rnv207
DO - 10.1093/imrn/rnv207
M3 - Article
AN - SCOPUS:84977119411
SN - 1073-7928
VL - 2016
SP - 2748
EP - 2812
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 9
ER -