{"paper":{"title":"Normal bundles of rational curves on complete intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eric Riedl, Izzet Coskun","submitted_at":"2017-05-23T17:52:14Z","abstract_excerpt":"Let $X \\subset \\mathbb{P}^n$ be a general Fano complete intersection of type $(d_1,\\dots, d_k)$. If at least one $d_i$ is greater than $2$, we show that $X$ contains rational curves of degree $e \\leq n$ with balanced normal bundle. If all $d_i$ are $2$ and $n\\geq 2k+1$, we show that $X$ contains rational curves of degree $e \\leq n-1$ with balanced normal bundle. As an application, we prove a stronger version of the theorem of Z. Tian \\cite{Tian}, Q. Chen and Y. Zhu \\cite{ChenZhu} that $X$ is separably rationally connected by exhibiting very free rational curves in $X$ of optimal degrees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08441","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"}