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

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

Research output: Research - peer-reviewArticle

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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 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.

LanguageEnglish (US)
Pages2748-2812
Number of pages65
JournalInternational Mathematics Research Notices
Volume2016
Issue number9
DOIs
StatePublished - 2016

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Desingularization
Minor
Arbitrary
Zero
Derived Category
Faithful
Generator

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Non-commutative Desingularization of Determinantal Varieties, II : Arbitrary Minors. / Buchweitz, Ragnar Olaf; Leuschke, Graham J.; Van Den Bergh, Michel.

In: International Mathematics Research Notices, Vol. 2016, No. 9, 2016, p. 2748-2812.

Research output: Research - peer-reviewArticle

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