{"paper":{"title":"Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gianluca Occhetta, Kiwamu Watanabe, Luis Eduardo Sol\\'a Conde, Roberto Mu\\~noz","submitted_at":"2013-04-14T17:28:39Z","abstract_excerpt":"A Fano manifold $X$ with nef tangent bundle is of flag-type if it has the same type of elementary contractions as a complete flag manifold. In this paper we present a method to associate a Dynkin diagram $\\mathcal{D}(X)$ with any such $X$, based on the numerical properties of its contractions. We then show that $\\mathcal{D}(X)$ is the Dynkin diagram of a semisimple Lie group. As an application we prove that Campana-Peternell conjecture holds when $X$ is a flag-type manifold whose Dynkin diagram is $A_n$ ($X$ is shown to be the complete flag in $\\mathbb{P}^n$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3928","kind":"arxiv","version":3},"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"}