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Invariant curves for holomorphic foliations on singular surfaces

Edileno de Almeida Santos Instituto de Ciência, Engenharia e Tecnologia, Universidade Federal dos Vales do Jequitinhonha e Mucuri (UFVJM), Teófilo Otoni, MG, Brazil

Complex Variables and Complex Analysis mathscidoc:2203.08002

Arkiv for Matematik, 58, (1), 179-195, 2020.4
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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@inproceedings{edileno2020invariant,
  title={Invariant curves for holomorphic foliations on singular surfaces},
  author={Edileno de Almeida Santos},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310171642915510939},
  booktitle={Arkiv for Matematik},
  volume={58},
  number={1},
  pages={179-195},
  year={2020},
}
Edileno de Almeida Santos. Invariant curves for holomorphic foliations on singular surfaces. 2020. Vol. 58. In Arkiv for Matematik. pp.179-195. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310171642915510939.
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