On a Mattei-Salem theorem

Arturo Fernández-Pérez; Nancy Saravia-Molina

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arXiv · 2408.10767

On a Mattei-Salem theorem

Arturo Fernández-Pérez·Nancy Saravia-Molina

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Abstract

We investigate the relationship between the valuations of a germ of a singular foliation $\mathcal{F}$ on the complex plane and those of a balanced equation of separatrices for $\mathcal{F}$, extending a theorem by Mattei-Salem. Under certain conditions, we also derive inequalities involving the valuation, tangency excess, and degree of a holomorphic foliation $\mathcal{F}$ on the complex projective plane.

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Arturo Fernández-Pérez, Nancy Saravia-Molina. 2024-08-20. On a Mattei-Salem theorem. https://arxiv.org/abs/2408.10767

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