On a Mattei–Salem theorem

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.