Logarithmic Models for Non-Dicritical Foliations

TL;DR

This paper proves that for certain complex holomorphic foliations without saddle-nodes, there exists a unique logarithmic model that captures their local structure.

Contribution

It establishes the existence and essential uniqueness of logarithmic models for non-dicritical singular holomorphic foliations of codimension one.

Findings

Existence of a logarithmic model for the foliations.

Essential uniqueness of the logarithmic model.

Applicable to foliations without saddle-nodes.

Abstract

We show the existence of an essentially unique logarithmic model for any germ of non-dicritical singular holomorphic foliation of codimension one in $({\mathbb C}^n,0)$ without saddle-nodes.