{"paper":{"title":"Genera of non-algebraic leaves of polynomial foliations of $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Nataliya Goncharuk, Yury Kudryashov","submitted_at":"2014-07-29T20:27:51Z","abstract_excerpt":"In this article, we prove two results. First, we construct a dense subset in the space of polynomial foliations of degree $n$ such that each foliation from this subset has a leaf with at least $\\frac{(n+1)(n+2)}2-4$ handles. Next, we prove that for a generic foliation invariant under the map $(x, y)\\mapsto (x, -y)$ all leaves have infinitely many handles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7878","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"}