{"paper":{"title":"Birational geometry of Fano direct products","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Aleksandr V. Pukhlikov","submitted_at":"2004-05-01T19:59:03Z","abstract_excerpt":"We prove birational superrigidity of direct products $V=F_1\\times...\\times F_K$ of primitive Fano varieties of the following two types: either $F_i\\subset{\\mathbb P}^M$ is a general hypersurface of degree $M$, $M\\geq 6$, or $F_i\\stackrel{\\sigma}{\\to}{\\mathbb P}^M$ is a general double space of index 1, $M\\geq 3$. In particular, each structure of a rationally connected fiber space on $V$ is given by a projection onto a direct factor. The proof is based on the connectedness principle of Shokurov and Koll\\' ar and the technique of hypertangent divisors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405011","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"}