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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 | Publisher: | OXFORD UNIV PRESS | Source: | INTERNATIONAL MATHEMATICS RESEARCH NOTICES,(9), p. 2748-2812 | 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. | Document URI: | http://hdl.handle.net/1942/22057 | ISSN: | 1073-7928 | e-ISSN: | 1687-0247 | DOI: | 10.1093/imrn/rnv207 | ISI #: | 000379774900006 | Rights: | © The Author(s) 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2017 |
Appears in Collections: | Research publications |
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