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April 2020 Invariant curves for holomorphic foliations on singular surfaces
Edileno de Almeida Santos
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Ark. Mat. 58(1): 179-195 (April 2020). DOI: 10.4310/ARKIV.2020.v58.n1.a11


The Separatrix Theorem of C. Camacho and P. Sad says that there exists at least one invariant curve (separatrix) passing through the singularity of a germ of holomorphic foliation on complex surface, when the surface underlying the foliation is smooth or when it is singular and the dual graph of resolution surface singularity is a tree. Under some assumptions, we obtain existence of separatrix even when the resolution dual graph of the surface singular point is not a tree. It will be necessary to require an extra condition of the foliation, namely, absence of saddle-node in its reduction of singularities.


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Edileno de Almeida Santos. "Invariant curves for holomorphic foliations on singular surfaces." Ark. Mat. 58 (1) 179 - 195, April 2020.


Received: 7 November 2018; Revised: 10 September 2019; Published: April 2020
First available in Project Euclid: 16 January 2021

Digital Object Identifier: 10.4310/ARKIV.2020.v58.n1.a11

Primary: 37F75

Keywords: birational geometry , foliations , invariant curves

Rights: Copyright © 2020 Institut Mittag-Leffler


Vol.58 • No. 1 • April 2020
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