{"paper":{"title":"Cylinders in del Pezzo fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrien Dubouloz (IMB), Takashi Kishimoto","submitted_at":"2016-07-04T12:09:01Z","abstract_excerpt":"We show that a del Pezzo fibration $\\pi$ : V $\\rightarrow$ W of degre d contains a vertical open cylinder, that is, an open subset whose intersection with the generic fiber of $\\pi$ is isomorphic to $Z\\times\\mathbb{A}_{K}^{1}$ for some quasi-projective variety Z defined over the function field K of W , if and only if d $\\ge$ 5 and $\\pi$ : V $\\rightarrow$ W admits a rational section. We also construct twisted cylinders in total spaces of threefold del Pezzo fibrations $\\pi$ : V $\\rightarrow$ P 1 of degree d $\\le$ 4."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00840","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"}