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Dicritical nilpotent holomorphic foliations

  • * Corresponding author: Jorge Mozo-Fernández

    * Corresponding author: Jorge Mozo-Fernández 
This work was funded by the Dirección de Gestión de la Investigación at the PUCP through grant DGI-2015-1-0045, and by the Ministerio de Economía y Competitividad from Spain, under Projects "Álgebra y Geometría en Dinámica Real y Compleja Ⅲ" (Ref.: MTM2013-46337-C2-1-P) and "Álgebra y geometr ía en sistemas dinámicos y foliaciones singulares" (Ref: MTM2016-77642-C2-1-P).
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  • We study in this paper several properties concerning singularities of foliations in $ {\left( {{\mathbb{C}}^{3}}\rm{,}\bf{0} \right)}$ that are pull-back of dicritical foliations in $ {\left( {{\mathbb{C}}^{2}}\rm{,}\bf{0} \right)}$. Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in $ {\left( {{\mathbb{C}}^{2}}\rm{,}\bf{0} \right)}$, the adaptations are not straightforward.

    Mathematics Subject Classification: Primary: 37F75; Secondary: 32S65.


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  • Figure 1.  The image of a closed leaf is closed

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