AI 中文总结
该研究探讨射影三维空间上二次叶状结构空间的例外分支的几何学，证明其含四个维数均为12的不可约分支，并明确各分支的轨道特征。
AI 中文摘要
我们研究射影三维空间$\boldsymbol{\text{P}^3}$上二次余维一叶状结构的空间$\boldsymbol{\text{F}(2,\boldsymbol{\text{P}^3})}$的例外分支，描述其边界的几何学并证明它有四个不可约分支，所有分支的维数均为12。其中三个分支包含由$(1,1,2)$型对数叶状结构的轨道构成的稠密子集，第四个分支包含从$\boldsymbol{\text{P}^2}}$拉回型叶状结构的族，其轨道的维数为11。
英文摘要
We study the exceptional component of the space $\mathbb{F}(2,\mathbb{P}^3)$, of codimension-one foliations of degree two on $\mathbb{P}^3$. We describe the geometry of its boundary and prove that it has four irreducible components, all of dimension $12$. Three of these components contain a dense subset given by the orbit of a logarithmic foliation of type $(1,1,2)$, while the fourth contains a family of pull-back type foliations from $\mathbb{P}^2$ whose orbits have dimension $11$.
