English

Holomorphic foliations tangent to Rolle-pfaffian hypersurfaces

Complex Variables 2024-08-08 v1 Dynamical Systems

Abstract

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.

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Cite

@article{arxiv.2408.03914,
  title  = {Holomorphic foliations tangent to Rolle-pfaffian hypersurfaces},
  author = {Arturo Fernández-Pérez and Rogério Mol and Rudy Rosas},
  journal= {arXiv preprint arXiv:2408.03914},
  year   = {2024}
}

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23 pages