{"paper":{"title":"The action of the Cremona group on rational curves of $ \\mathbb{P}^{3} $","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elena Angelini, Massimiliano Mella","submitted_at":"2015-05-04T09:11:11Z","abstract_excerpt":"A Cremona transformation is a birational self-map of the projective space $ \\mathbb{P}^{n} $. Cremona transformations of $ \\mathbb{P}^{n} $ form a group and this group has a rational action on subvarieties of $ \\mathbb{P}^{n} $ and hence on its Hilbert scheme. We study this action on the family of rational curves of $ \\mathbb{P}^{3} $ and we prove the rectifiability of any one dimensional family. This shows that any uniruled surface is Cremona equivalent to a scroll and it answers a question of Bogomolov-B\\\"ohning related to the study of uniformly rational varieties. We provide examples of inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00563","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"}