Isolated invariant curves of a foliation

Abstract

We bound the equisingularity type of the set of isolated separatrices of a holomorphic foliation $\mathcal F$ of $({\mathbb C}^2,0)$ in terms of the Milnor number of $\mathcal F$. This result gives a bound for the degree of an algebraic invariant curve $C \subset {\mathbb P}^{2}_{\mathbb C}$ of a foliation $\mathcal G$ of ${\mathbb P}^{2}_{\mathbb C}$ in terms of the degree of $\mathcal G$, provided that all the branches of $C$ are isolated separatrices.

Locations

• Proceedings of the American Mathematical Society - View - PDF