论文标题
$ \ mathbb {cp}^3 $ of gug $ 2 $的粮食
Foliations on $\mathbb{CP}^3$ of degree $2$ that have a line as singular set
论文作者
论文摘要
在这项工作中，我们对$ \ mathbb {cp}^3 $ of Codimension 1和$ 2 $的叶子进行分类，这些叶子具有单一的套件。为了实现这一目标，我们对组件进行完整的描述。我们证明，特殊成分的边界只有3个叶子以更改坐标，并且该边界包含在对数分量中。最后，我们在$ \ mathbb {cp}^3 $上构建了Codimension 1和$ s \ geq 3 $的叶子示例，它们具有单一的单位套件，因此它们组成了一个具有合理的$ s+s+1 $组成部分的家庭，或者它们是对数中的一些人，其中一些人是最小的，其中一些人具有最小的一体化程度。
In this work we classify foliations on $\mathbb{CP}^3$ of codimension 1 and degree $2$ that have a line as singular set. To achieve this, we do a complete description of the components. We prove that the boundary of the exceptional component has only 3 foliations up to change of coordinates, and this boundary is contained in a logarithmic component. Finally we construct examples of foliations on $\mathbb{CP}^3$ of codimension 1 and degree $s \geq 3$ that have a line as singular set and such that they form a family with a rational first integral of degree $s+1$ or they are logarithmic foliations where some of them have a minimal rational first integral of degree not bounded.
