RT info:eu-repo/semantics/article
T1 The local Poincaré problem for irreducible branches
A1 Cano Torres, José María
A1 Fortuny Ayuso, Pedro
A1 Ribón, Javier
A1 
K1 Holomorphic foliation, Poincaré problem, plane branch, separatrix, Puiseux parametrization.
K1 1204 Geometría
K1 1201 Álgebra
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 holomorphicinvariant curve γ. We provide a lower bound for the vanishing multiplicityof F at the origin in terms of the equisingularity class of γ. Moreover, weshow that such a lower bound is sharp. Finally, we characterize the typesof dicritical singularities for which the multiplicity of F can be boundedin terms of that of γ, and provide an explicit bound in this case.
PB European Mathematical Society Publishing House
SN 0213-2230
YR 2020
FD 2020
LK https://uvadoc.uva.es/handle/10324/65518
UL https://uvadoc.uva.es/handle/10324/65518
LA eng
NO Revista Matematica Iberoamericana, 2021, Volume 37, Issue 6, Pages 2229 - 2244
DS UVaDOC
RD 07-ago-2024