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oai:uvadoc.uva.es:10324/655182024-12-04T07:53:35Zcom_10324_1129com_10324_931com_10324_894col_10324_1193

2024-02-01T13:15:17Z urn:hdl:10324/65518 The local Poincaré problem for irreducible branches Cano Torres, José María Fortuny Ayuso, Pedro Ribón, Javier Cano Torres, José María Let F be a germ of holomorphic foliation defined in a neigh- borhood of the origin of C2 that has a germ of irreducible holomorphic invariant curve γ. We provide a lower bound for the vanishing multiplicity of F at the origin in terms of the equisingularity class of γ. Moreover, we show that such a lower bound is sharp. Finally, we characterize the types of dicritical singularities for which the multiplicity of F can be bounded in terms of that of γ, and provide an explicit bound in this case. 2024-02-01T13:15:17Z 2024-02-01T13:15:17Z 2020 info:eu-repo/semantics/article Revista Matematica Iberoamericana, 2021, Volume 37, Issue 6, Pages 2229 - 2244 0213-2230 https://uvadoc.uva.es/handle/10324/65518 10.4171/rmi/1260 2229 6 2244 Revista Matemática Iberoamericana 37 eng https://doi.org/10.4171/rmi/1260 info:eu-repo/semantics/restrictedAccess Real Sociedad Matemática Española Published by EMS Press European Mathematical Society Publishing House