Holomorphic foliations tangent to Rolle-pfaffian hypersurfaces

In this paper we study germs of holomorphic foliations, at the origin of the complex plane, tangent to Pfaffian hypersurfaces - integral hypersurfaces of real analytic 1-forms - satisfying the Rolle-Khovanskii condition. This hypothesis leads us to conclude that such a foliation is defined by a clos...

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Published in:arXiv.org 2024-08
Main Authors: Fernández-Pérez, Arturo, Mol, Rogério, Rosas, Rudy
Format: Article
Language:English
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Summary:In this paper we study germs of holomorphic foliations, at the origin of the complex plane, tangent to Pfaffian hypersurfaces - integral hypersurfaces of real analytic 1-forms - satisfying the Rolle-Khovanskii condition. This hypothesis leads us to conclude that such a foliation is defined by a closed meromorphic 1-form, also allowing the classification of the simple models in its reduction of singularities.
ISSN:2331-8422