Cubic fourfolds containing a plane and a quantic del Pezzo surface

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dc.citation.firstpage181en_US
dc.citation.issueNumber2en_US
dc.citation.journalTitleAlgebraic Geometryen_US
dc.citation.lastpage193en_US
dc.citation.volumeNumber1en_US
dc.contributor.authorAuel, Asheren_US
dc.contributor.authorBernardara, Marcelloen_US
dc.contributor.authorBolognesi, Micheleen_US
dc.contributor.authorVárilly-Alvarado, Anthonyen_US
dc.date.accessioned2016-01-28T17:15:40Zen_US
dc.date.available2016-01-28T17:15:40Zen_US
dc.date.issued2014en_US
dc.description.abstractWe 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.en_US
dc.identifier.citationAuel, Asher, Bernardara, Marcello, Bolognesi, Michele, et al.. "Cubic fourfolds containing a plane and a quantic del Pezzo surface." <i>Algebraic Geometry,</i> 1, no. 2 (2014) Foundation Compositio Mathematica: 181-193. http://dx.doi.org/10.14231/AG-2014-010.en_US
dc.identifier.doihttp://dx.doi.org/10.14231/AG-2014-010en_US
dc.identifier.urihttps://hdl.handle.net/1911/88219en_US
dc.language.isoengen_US
dc.publisherFoundation Compositio Mathematicaen_US
dc.rightsThis 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.en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc/3.0/en_US
dc.subject.keywordcubic fourfolden_US
dc.subject.keywordquadric surface bundleen_US
dc.subject.keywordK3 surfaceen_US
dc.subject.keywordrationalityen_US
dc.subject.keywordderived categoryen_US
dc.titleCubic fourfolds containing a plane and a quantic del Pezzo surfaceen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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