{"paper":{"title":"Around the Mukai conjecture for Fano manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kento Fujita","submitted_at":"2014-09-30T08:37:01Z","abstract_excerpt":"As a generalization of the Mukai conjecture, we conjecture that the Fano manifolds $X$ which satisfy the property $\\rho_X(r_X-1)\\geq\\dim X-1$ have very special structure, where $\\rho_X$ is the Picard number of $X$ and $r_X$ is the index of $X$. In this paper, we classify those $X$ if $\\rho_X\\leq 3$ or $\\dim X\\leq 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8433","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"}