We prove that, if $n\geq 3$, a singular foliation $\mathcal{F}$ on $\mathbb P^n$ which can be written as pull-back, where $\mathcal{G}$ is a foliation in $ {\mathbb P^2}$ of degree $d\geq2$ with one or three invariant lines in general position and $f:{\mathbb P^n}--->{\mathbb P^2}$, $deg(f)=ν\geq2,$ is an appropriated rational map, is stable under holomorphic deformations. As a consequence we conclude that the closure of the sets $\{\mathcal {F}= f^{*}(\mathcal{G})\}$ are new irreducible components of the space of holomorphic foliations of certain degrees.
Holomorphic foliations of degree two and arbitrary dimension
Dipartimento di Matematica, Università degli Studi di Bari（巴里大学数学系）；Universidade Estadual de Campinas (UNICAMP) Instituto de Matemática, Estatística e Computação Científica (IMECC) Departamento de Matemática（坎皮纳斯州立大学数学、统计与科学计算研究所数学系）；Departamento de Matemática Centro de Ciências Exatas e da Natureza Universidade Federal de Pernambuco（伯南布哥联邦大学自然与精确科学中心数学系）
Almost nef regular foliations and Fujita's decomposition of reflexive sheaves
本文研究几乎非正则叶理。本文给出了具有几乎nef正则叶理的光滑射影簇$X$的结构定理：$X$允许一个具有有理连通纤维的光滑态射$f: X \rightarrow Y$，使得$\mathcal{F}$是$Y$上数值平坦正则叶理的拉回.此外，$f$被表征为$\mathcal{F}$的代数部分的相对MRC纤维化。作为推论，有理连通簇的几乎nef切丛一般是充分的。为了证明，我们推广了Fujita分解定理。作为一个副产品，我们证明了$f_{*}(mK_{X/Y})$的自反壳是一个埃尔米特平坦向量丛和一般充足的自反层的任何代数纤维空间$f : X \rightarrow Y$的直和。我们还研究了具有nef反典范丛的叶理。
