{"paper":{"title":"Existence des diviseurs dicritiques, d'apr\\`es S.S.Abhyankar","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Guillermo Moreno-Socias, Micka\\\"el Matusinski, Vincent Cossart","submitted_at":"2012-04-03T09:12:49Z","abstract_excerpt":"In geometric terms, given a singular foliation of the plane, a dicritical divisor is (whenever it exists) an irreducible component of the exceptional divisor which is transverse to the foliation. Abhyankar gave recently a definition of the dicritical divisors which generalize and algebraicize the geometrical definition in the local case and the polynomial case. Following his work, we give a geometrical interpretation of these dicritical divisors and new proofs of their existence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0629","kind":"arxiv","version":2},"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"}