{"paper":{"title":"Second type foliations of codimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Gilberto Cuzzuol, Rog\\'erio Mol","submitted_at":"2017-08-02T11:40:36Z","abstract_excerpt":"In this article, for holomorphic foliations of codimension one at $(\\mathbb{C}^{3},0)$, we define the family of second type foliations. This is formed by foliations having, in the reduction process by blow-up maps, only well oriented singularities, meaning that the reduction divisor does not contain weak separatrices of saddle-node singularities. We prove that the reduction of singularities of a non-dicritical foliation of second type coincides with the desingularization of its set of separatrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00708","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"}