{"paper":{"title":"On cubic hypersurfaces of dimension seven and eight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Atanas Iliev, Laurent Manivel (IF)","submitted_at":"2011-02-17T16:14:28Z","abstract_excerpt":"Cubic sevenfolds are examples of Fano manifolds of Calabi-Yau type. We study them in relation with the Cartan cubic, the $E_6$-invariant cubic in $\\PP^{26}$. We show that a generic cubic sevenfold $X$ can be described as a linear section of the Cartan cubic, in finitely many ways. To each such \"Cartan representation\" we associate a rank nine vector bundle on $X$ with very special cohomological properties. In particular it allows to define auto-equivalences of the non-commutative Calabi-Yau threefold associated to $X$ by Kuznetsov. Finally we show that the generic eight dimensional section of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3618","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}