TY - JOUR AU - Cano Torres, José María AU - Fortuny Ayuso, Pedro AU - Ribón, Javier AU - PY - 2020 SN - 0213-2230 UR - https://uvadoc.uva.es/handle/10324/65518 AB - 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... LA - eng PB - European Mathematical Society Publishing House KW - Holomorphic foliation, Poincaré problem, plane branch, separatrix, Puiseux parametrization. TI - The local Poincaré problem for irreducible branches DO - 10.4171/rmi/1260 ER -