{"paper":{"title":"Conic-connected Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Russo, Paltin Ionescu","submitted_at":"2007-01-30T16:38:40Z","abstract_excerpt":"We study a particular class of rationally connected manifolds, $X\\subset \\p^N$, such that two general points $x,x' \\in X$ may be joined by a conic contained in $X$. We prove that these manifolds are Fano, with $b_2\\leq 2$. Moreover, a precise classification is obtained for $b_2=2$. Complete intersections of high dimension with respect to their multi-degree provide examples for the case $b_2=1$. The proof of the classification result uses a general characterization of rationality, in terms of suitable covering families of rational curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701885","kind":"arxiv","version":3},"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"}