{"paper":{"title":"Morse Theory and the topology of holomorphic foliations near an isolated singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Beatriz Lim\\'on, Jos\\'e Seade","submitted_at":"2011-05-18T21:13:44Z","abstract_excerpt":"Let $\\mathcal{F}$ be the germ at $\\mathbf{0} \\in \\mathbb{C}^n$ of a holomorphic foliation of dimension $d$, $1 \\leq d < n$, with an isolated singularity at $\\mathbf{0}$. We study its geometry and topology using ideas that originate in the work of Thom concerning Morse theory for foliated manifolds. Given $\\mathcal{F}$ and a real analytic function $g$ on $\\mathbb{C}^n$ with a Morse critical point of index 0 at $\\mathbf{0}$, we look at the corresponding polar variety $M= M(\\mathcal{F},g)$. These are the points of contact of the two foliations, where $\\mathcal{F}$ is tangent to the fibres of $g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3752","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"}