{"paper":{"title":"Singular holomorphic foliations by curves I: Integrability of holonomy cocycle in dimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.DS","authors_text":"Viet-Anh Nguyen","submitted_at":"2014-03-30T01:38:26Z","abstract_excerpt":"We study the holonomy cocycle H of a holomorphic foliation \\Fc by Riemann surfaces defined on a compact complex projective surface X satisfying the following two conditions:\n  1) its singularities E are all hyperbolic;\n  2) there is no holomorphic non-constant map \\C\\to X such that out of E the image of \\C is locally contained in a leaf.\n  Let T be a harmonic current tangent to \\Fc which does not give mass to any invariant analytic curve. Using the leafwise Poincar\\'e metric, we show that H is integrable with respect to T.\n  Consequently, we infer the existence of the Lyapunov exponent functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7688","kind":"arxiv","version":4},"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"}