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

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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2748-2812
Number of pages65
JournalInternational Mathematics Research Notices
Volume2016
Issue number9
DOIs
StatePublished - 2016

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Non-commutative Desingularization of Determinantal Varieties, II: Arbitrary Minors'. Together they form a unique fingerprint.

Cite this