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On Severi varieties as intersections of a minimum number of quadrics

dc.creatorVan Maldeghem, Hendrik
dc.creatorVictoor, Magali
dc.date2022-08-22
dc.date.accessioned2022-08-30T14:54:24Z
dc.date.available2022-08-30T14:54:24Z
dc.identifierhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/3105
dc.identifier10.56754/0719-0646.2402.0307
dc.identifier.urihttps://revistaschilenas.uchile.cl/handle/2250/206746
dc.descriptionLet \({\mathscr{V}}\) be a variety related to the second row of the Freudenthal-Tits Magic square in \(N\)-dimensional projective space over an arbitrary field. We show that there exist \(M\leq N\) quadrics intersecting precisely in \({\mathscr{V}}\) if and only if there exists a subspace of projective dimension \(N-M\) in the secant variety disjoint from the Severi variety. We present some examples of such subspaces of relatively large dimension. In particular, over the real numbers we show that the Cartan variety (related to the exceptional group \({E_6}\)\((\mathbb R)\)) is the set-theoretic intersection of 15 quadrics.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad de La Frontera. Temuco, Chile.en-US
dc.relationhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/3105/2204
dc.rightsCopyright (c) 2022 H. Van Maldeghem et al.en-US
dc.rightshttps://creativecommons.org/licenses/by-nc/4.0/en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 24 No. 2 (2022); 307–331en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 24 Núm. 2 (2022); 307–331es-ES
dc.source0719-0646
dc.source0716-7776
dc.subjectCartan varietyen-US
dc.subjectquadricsen-US
dc.subjectexceptional geometryen-US
dc.subjectSeveri varietyen-US
dc.subjectquaternion veronesianen-US
dc.titleOn Severi varieties as intersections of a minimum number of quadricsen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


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