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Title: Non-commutative Desingularization of Determinantal Varieties, II: Arbitrary Minors
Authors: Buchweitz, Ragnar-Olaf
Leuschke, Graham J.
van den Bergh, Michel
Issue Date: 2016
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 theexistence 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.
Notes: [Buchweitz, Ragnar-Olaf] Univ Toronto Scarborough, Dept Comp & Math Sci, Toronto, ON M1C 1A4, Canada. [Leuschke, Graham J.] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA. [Van den Bergh, Michel] Univ Hasselt, Dept WNI, B-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/22057
DOI: 10.1093/imrn/rnv207
ISI #: 000379774900006
ISSN: 1073-7928
Category: A1
Type: Journal Contribution
Validation: ecoom, 2017
Appears in Collections: Research publications

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