{"paper":{"title":"Varieties swept out by grassmannians of lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luis E. Sola Conde, Roberto Munoz","submitted_at":"2008-10-01T11:05:01Z","abstract_excerpt":"We classify complex projective varieties of dimension $2r \\geq 8$ swept out by a family of codimension two grassmannians of lines $\\mathbb{G}(1,r)$. They are either fibrations onto normal surfaces such that the general fibers are isomorphic to $\\G(1,r)$ or the grassmannian $\\mathbb{G}(1,r+1)$. The cases $r=2$ and $r=3$ are also considered in the more general context of varieties swept out by codimension two linear spaces or quadrics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0129","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"}