A codimension one singular holomorphic foliation is Newton non-degenerate if it satisfies some non-degeneracy conditions, in terms of its Newton polyhedra system. These conditions are similar to the ones of Kouchnirenko and Oka for the case of functions. We introduce the concept of logarithmic reduction of singularities and we prove that a foliation is Newton non-degenerate if and only if it admits a logarithmic reduction of singularities of a combinatorial nature.

中文翻译：

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牛顿非退化的叶状体和起伏

就其牛顿多面体系统而言，如果满足某些非简并性条件，则一维奇异全同叶型是牛顿非简并性。对于功能而言，这些条件类似于Kouchnirenko和Oka的条件。我们引入奇异性的对数降低的概念，并且证明并且仅当它允许组合性奇异性的对数降低时，叶才是牛顿非简并。