Isolated invariant curves of a foliation

Corral, Nuria; Fernández-Sánchez, Percy

doi:10.1090/S0002-9939-05-08044-5

Isolated invariant curves of a foliation
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by Nuria Corral and Percy Fernández-Sánchez PDF

Proc. Amer. Math. Soc. 134 (2006), 1125-1132 Request permission

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.

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