Non-commutative Desingularization of Determinantal Varieties, II: Arbitrary Minors

Ragnar Olaf Buchweitz, Graham J. Leuschke, Michel Van Den Bergh

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11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2748-2812
Number of pages65
JournalInternational Mathematics Research Notices
Issue number9
StatePublished - 2016

ASJC Scopus subject areas

  • General Mathematics


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