{"paper":{"title":"Projective varieties invariant by one-dimensional foliations","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Marcio G. Soares","submitted_at":"2000-09-01T00:00:00Z","abstract_excerpt":"This work concerns the problem of relating characteristic numbers of one-dimensional holomorphic foliations of P^n to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional holomorphic foliation F of M is a morphism \\Phi:L -> TM where L is a holomorphic line bundle on M. The singular set of F is the analytic subvariety sing(F) = {p : \\Phi(p)=0} and the leaves of F are the leaves of the nonsingular foliation induced by F on M-sing(F). If M is P^n then, since line bundles over P^n are classified by the Chern class c_1(L) in H^2(P^n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0009253","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"}