Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branched pull-back components of the space of codimension 1 foliations
  on $\mathbb P^n$   Let $\mathcal{F}$ be written as $ f^{*}\mathcal{G}$, where $\mathcal{G}$ is a
foliation in $ {\mathbb P^2}$ with three invariant lines in general position,
say $(XYZ)=0$, and $f:{\mathbb P^n}--->{\mathbb P^2}$,
$f=(F^\alpha_{0}:F^\beta_{1}:F^\gamma_{2})$ is a nonlinear rational map. Using
local stability results of singular holomorphic foliations, we prove that: if
$n\geq 3$, the foliation $\mathcal{F}$ is globally stable under holomorphic
deformations. As a consequence we obtain new irreducible componentes for the
space of codimension one foliations on $\mathbb P^n$. We present also a result
which characterizes holomorphic foliations on ${\mathbb P^n}, n\geq 3$ which
can be obtained as a pull back of foliations on $ {\mathbb P^2}$ of degree
$d\geq2$ with three invariant lines in general position.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics