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Isolated invariant curves of a foliation

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.

Autor(es):
Corral, Nuria;
Fernández Sánchez, Percy.
Año: 2006
Título de la revista: Proceedings of the American Mathematical Society
Volumen: 134
Página inicial - Página final: 1125-1132
ISSN: 1088-6826(online) 0002-9939(print)
Url: http://www.ams.org/journals/proc/2006-134-04/S0002-9939-05-08044-5/S0002-9939-05-08044-5.pdf