{"paper":{"title":"Absolutely $k$-convex domains and holomorphic foliations on homogeneous manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.AG","authors_text":"Arturo Fern\\'andez-P\\'erez, Mauricio Corr\\^ea Jr","submitted_at":"2014-03-17T22:08:55Z","abstract_excerpt":"We consider a holomorphic foliation $\\mathcal{F}$ of codimension $k\\geq 1$ on a homogeneous compact K\\\"ahler manifold $X$ of dimension $n>k$. Assuming that the singular set $Sing(\\mathcal{F})$ of $\\mathcal{F}$ is contained in an absolutely $k$-convex domain $U\\subset X$, we prove that the determinant of normal bundle $\\det(N_{\\mathcal{F}})$ of $\\mathcal{F}$ cannot be an ample line bundle, provided $[n/k]\\geq 2k+3$. Here $[n/k]$ denotes the largest integer $\\leq n/k.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4286","kind":"arxiv","version":6},"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"}