Newton Non-degenerate Foliations and Blowing-ups

Abstract

A codimension one singular holomorphic foliation is Newton non-degenerate if it satisfies the classical conditions of Kouchnirenko and Oka, in terms of its Newton polyhedra system. In this paper we prove that a foliation is Newton non-degenerate if and only if it admits a logarithmic reduction of singularities of a combinatorial nature.