{"paper":{"title":"Foliations by Curves with Curves as Singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.AG","authors_text":"Arturo Fernandez Perez, Gilcione Nonato Costa, Maur\\'icio Corr\\^ea Jr, Renato Vidal Martins","submitted_at":"2012-09-25T14:22:39Z","abstract_excerpt":"Let $\\mathcal F$ be a holomorphic one-dimensional foliation on $\\mathbb{P}^n$ such that the components of its singular locus $\\Sigma$ are curves $C_i$ and points $p_j$. We determine the number of $p_j$, counted with multiplicities, in terms of invariants of $\\mathcal F$ and $C_i$, assuming that $\\mathcal F$ is special along the $C_i$. Allowing just one nonzero dimensional component on $\\Sigma$, we also prove results on when the foliation happens to be determined by its singular locus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5618","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"}