# Lenses on very curved zones of a singular foliation of $C^2$

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Abstract : We renormalize, using suitable lenses, small domains of a singular holomorphic foliation of $C^2$ where the curvature is concentrated. At a proper scale, the leaves are almost translates of a graph that we will call "profile". When the leaves of the foliations are levels $f = \lambda$ where $f$ is a polynomial in 2 variables, this graph is polynomial. Finally we will indicate how our methods may be adapted to study levels of polynomials and 1-forms in $C^3$
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https://hal.archives-ouvertes.fr/hal-01674696
Contributor : Imb - Université de Bourgogne <>
Submitted on : Wednesday, January 3, 2018 - 2:17:05 PM
Last modification on : Friday, October 19, 2018 - 1:18:59 PM

### Citation

Rémi Langevin, Jean-Claude Sifre. Lenses on very curved zones of a singular foliation of $C^2$. Topology and its Applications, Elsevier, 2018, 234, pp.397-414. ⟨10.1016/j.topol.2017.11.019⟩. ⟨hal-01674696⟩

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