Construction of invariant curves for singular holomorphic vector fields

Abstract:

Camacho and Sad proved the existence of invariant analytic curves for germs of singular holomorphic foliations ${\mathcal {F}}$ over a two dimensional complex analytic variety $M$. Their proof is only of existential nature. Here we provide a simple constructive proof by giving criteria to choose a singular point at each blowing-up that follows an analytic invariant curve.