On a Mattei–Salem theorem
Annales Polonici Mathematici
MSC: Primary 32S65; Secondary 37F75
DOI: 10.4064/ap240820-22-12
Published online: 26 February 2025
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.
