关于(C^3,0)中的拟普通尖点叶状结构

On codimension one foliations with prescribed cuspidal separatrix

In this paper, we will construct a pre-normal form for germs of codimension one holomorphic foliation having a particular type of separatrix, of cuspidal type. We will also give a sufficient condition, in the quasi-homogeneous, three-dimensional case, for these foliations to be of generalized surface type.

Analytic classification of a class of cuspidal foliations in $({\mathbb C}^3,0)$

In this article we study the analytic classification of certain types of quasi-homogeneous cuspidal holomorphic foliations in $(\CC^3,{\bf 0})$ via the essential holonomy defined over one of the components of the exceptional divisor that appears in the reduction of the singularities of the foliation.

Characterization of second type plane foliations using Newton polygons

In this article we characterize the foliations that have the same Newton polygon that their union of formal separatrices, they are the foliations called of the second type. In the case of cuspidal foliations studied by Loray, we precise this characterization using the Poincaré-Hopf index. This index also characterizes the cuspidal foliations having the same desingularization that the union of its separatrices. Finally we give necessary and sufficient conditions when these cuspidal foliations are generalized curves, and a characterization when they have only one separatrix.

复数维$(\mathbb{C}^n,\mathbf{0})$上的 nilpotent 光滑叶结构

Nilpotent Holomorphic Foliations on $(\mathbb{C}^n,\mathbf{0})$

本文研究复数维$(\mathbb{C}^n,\mathbf{0})$上的nilpotent光滑叶结构，通过分析其与Takens正常型的关系，提出新的准则以判断叶结构是否为广义超曲面类型。

关于与奇异二阶常微分方程相关的全纯叶状结构的旗（flags）

On flags of holomorphic foliations associated with singular second-order ordinary differential equations

本文研究与二阶常微分方程相关的全纯叶状结构2-旗，分析其奇点集性质，给出容许该结构的二阶方程分类，提出高维2-旗芽构造方法，并证明二阶及以上方程形式上均对应$\boldsymbol{\rm \bf C}^3$原点处的2-旗芽。