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arXiv · 1703.10749

Dicritical nilpotent holomorphic foliations

Percy Fernández Sánchez·Jorge Mozo Fernández·Hernán Neciosup
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Abstract

We study in this paper several properties concerning singularities of foliations in $(\mathbb{C}^3,\mathbf{0})$ that are pull-back of dicritical foliations in $(\mathbb{C}^2,\mathbf{0})$. 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 $(\mathbb{C}^2,\mathbf{0})$, the adaptations are not straightforward.

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Percy Fernández Sánchez, Jorge Mozo Fernández, Hernán Neciosup. 2017-03-31. Dicritical nilpotent holomorphic foliations. https://arxiv.org/abs/1703.10749

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