The differentiable-invariance of the algebraic multiplicity of a holomorphic vector field (Q847623)

The algebraic multiplicity of a holomorphic vector field in the plane with a singularity at the origin is a topological invariant, if the foliation defined by the field is a generalised curve [\textit{C. Camacho, A. Lins Neto, P. Sad}, J. Differ. Geom. 20, 143--174 (1984; Zbl 0576.32020)]. The same is true in the dicritical case. The author proves in the non-dicritical case that the multiplicity is preserved by topological equivalences, that are differentiable at the origin.