Newton Non-degenerate Foliations and Blowing-ups

Abstract

A codimension one singular holomorphic foliation is Newton nondegenerate 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.