{"paper":{"title":"Birationally rigid Fano complete intersections. II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Aleksandr Pukhlikov","submitted_at":"2011-10-10T14:26:55Z","abstract_excerpt":"We prove that a generic (in the sense of Zariski topology) Fano complete intersection $V$ of the type $(d_1,...,d_k)$ in ${\\mathbb P}^{M+k}$, where $d_1+...+d_k=M+k$, is birationally superrigid if $M\\geq 7$, $M\\geq k+3$ and $\\mathop{\\rm max} \\{d_i\\}\\geq 4$. In particular, on the variety $V$ there is exactly one structure of a Mori fibre space (or a rationally connected fibre space), the groups of birational and biregular self-maps coincide, $\\mathop{\\rm Bir} V= \\mathop{\\rm Aut} V$, and the variety $V$ is non-rational. This fact covers a considerably larger range of complete intersections than "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2052","kind":"arxiv","version":1},"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"}