Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/36126
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dc.contributor.authorSPENKO, Spela-
dc.contributor.authorVAN DEN BERGH, Michel-
dc.contributor.authorBell, Jason P.-
dc.date.accessioned2021-12-10T09:36:04Z-
dc.date.available2021-12-10T09:36:04Z-
dc.date.issued2022-
dc.date.submitted2021-12-08T10:21:23Z-
dc.identifier.citationMathematische Zeitschrift, 300 (1), p. 1055-1068-
dc.identifier.urihttp://hdl.handle.net/1942/36126-
dc.description.abstractWe show that all toric noncommutative crepant resolutions (NCCRs) of affine GIT quotients of "weakly symmetric" unimodular torus representations are derived equivalent. This yields evidence for a non-commutative extension of a well known conjecture by Bondal and Orlov stating that all crepant resolutions of a Gorenstein singularity are derived equivalent. We prove our result by showing that all toric NCCRs of the affine GIT quotient are derived equivalent to a fixed Deligne-Mumford GIT quotient stack associated to a generic character of the torus. This extends a result by Halpern-Leistner and Sam which showed that such GIT quotient stacks are a geometric incarnation of a family of specific toric NCCRs constructed earlier by the authors.-
dc.description.abstractWe show that all toric noncommutative crepant resolutions (NCCRs) of affine GIT quotients of "weakly symmetric" unimodular torus representations are derived equivalent. This yields evidence for a non-commutative extension of a well known conjecture by Bondal and Orlov stating that all crepant resolutions of a Gorenstein singularity are derived equivalent. We prove our result by showing that all toric NCCRs of the affine GIT quotient are derived equivalent to a fixed Deligne-Mumford GIT quotient stack associated to a generic character of the torus. This extends a result by Halpern-Leistner and Sam which showed that such GIT quotient stacks are a geometric incarnation of a family of specific toric NCCRs constructed earlier by the authors.-
dc.description.sponsorshipEuropean Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant [665501]; Research Foundation Flanders (FWO)FWO [665501, G0D8616N]-
dc.language.isoen-
dc.publisherSPRINGER HEIDELBERG-
dc.rightsThe Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021-
dc.titleOn the noncommutative Bondal–Orlov conjecture for some toric varieties-
dc.typeJournal Contribution-
dc.identifier.epage1068-
dc.identifier.issue1-
dc.identifier.spage1055-
dc.identifier.volume300-
local.format.pages14-
local.bibliographicCitation.jcatA1-
dc.description.notesVan den Bergh, M (corresponding author), Vrije Univ Brussel, Dept Wiskunde, Pl Laan 2, B-1050 Ixelles, Belgium.; Van den Bergh, M (corresponding author), Univ Hasselt, Dept WNI, Univ Campus, B-3590 Diepenbeek, Belgium.-
dc.description.notesspela.spenko@vuh.ac.be; michel.vandenbergh@uhasselt.be;-
dc.description.notesjpbell@uwaterloo.ca-
local.publisher.placeTIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY-
local.type.refereedRefereed-
local.type.specifiedArticle-
local.type.programmeH2020-
local.relation.h2020665501-
dc.identifier.doi10.1007/s00209-021-02910-8-
dc.identifier.isiWOS:000722086200001-
local.provider.typewosris-
local.uhasselt.uhpubyes-
local.description.affiliation[Spenko, Spela; Van den Bergh, Michel] Vrije Univ Brussel, Dept Wiskunde, Pl Laan 2, B-1050 Ixelles, Belgium.-
local.description.affiliation[Van den Bergh, Michel] Univ Hasselt, Dept WNI, Univ Campus, B-3590 Diepenbeek, Belgium.-
local.description.affiliation[Bell, Jason P.] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada.-
local.uhasselt.internationalyes-
item.accessRightsOpen Access-
item.contributorSPENKO, Spela-
item.contributorVAN DEN BERGH, Michel-
item.contributorBell, Jason P.-
item.fullcitationSPENKO, Spela; VAN DEN BERGH, Michel & Bell, Jason P. (2022) On the noncommutative Bondal–Orlov conjecture for some toric varieties. In: Mathematische Zeitschrift, 300 (1), p. 1055-1068.-
item.validationecoom 2023-
item.fulltextWith Fulltext-
crisitem.journal.issn0025-5874-
crisitem.journal.eissn1432-1823-
Appears in Collections:Research publications
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