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dc.contributor.authorAuel, Asher
Bernardara, Marcello
Bolognesi, Michele
Várilly-Alvarado, Anthony
dc.date.accessioned 2016-01-28T17:15:40Z
dc.date.available 2016-01-28T17:15:40Z
dc.date.issued 2014
dc.identifier.citation Auel, Asher, Bernardara, Marcello, Bolognesi, Michele, et al.. "Cubic fourfolds containing a plane and a quantic del Pezzo surface." Algebraic Geometry, 1, no. 2 (2014) Foundation Compositio Mathematica: 181-193. http://dx.doi.org/10.14231/AG-2014-010.
dc.identifier.urihttps://hdl.handle.net/1911/88219
dc.description.abstract We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontriviality of the Brauer class β of the even Clifford algebra over the K3 surface S of degree 2 arising from X. Specifically, we show that in the moduli space of cubic fourfolds, the intersection of divisors C8 ∩ C14 has five irreducible components. In the component corresponding to the existence of a tangent conic, we prove that the general member is both pfaffian and has β nontrivial. Such cubic fourfolds provide twisted derived equivalences between K3 surfaces of degrees 2 and 14, hence further corroboration of Kuznetsov’s derived categorical conjecture on the rationality of cubic fourfolds.
dc.language.iso eng
dc.publisher Foundation Compositio Mathematica
dc.rights This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited.
dc.rights.urihttp://creativecommons.org/licenses/by-nc/3.0/
dc.title Cubic fourfolds containing a plane and a quantic del Pezzo surface
dc.type Journal article
dc.contributor.funder National Science Foundation
dc.citation.journalTitle Algebraic Geometry
dc.subject.keywordcubic fourfold
quadric surface bundle
K3 surface
rationality
derived category
dc.citation.volumeNumber 1
dc.citation.issueNumber 2
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.14231/AG-2014-010
dc.identifier.grantID MSPRF DMS-0903039 (National Science Foundation)
dc.identifier.grantID DMS-1103659 (National Science Foundation)
dc.type.publication publisher version
dc.citation.firstpage 181
dc.citation.lastpage 193


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This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited.
Except where otherwise noted, this item's license is described as This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited.