Linear Pullback Components of the Space of Codimension One Foliations

The space of holomorphic foliations of codimension one and degree $d\geq 2$ in $\mathbb{P}^n$ ($n\geq 3$) has an irreducible component whose general element can be written as a pullback $F^*\mathcal{F}$, where $\mathcal{F}$ is a general foliation of degree $d$ in $\mathbb{P}^2$ and $F:\mathbb{P}^n\dashrightarrow \mathbb{P}^2$ is a general rational linear map. We give a polynomial formula for the degrees of such components.
Comment: This is a pre-print of an article published in Bulletin of the Brazilian Mathematical Society, New Series (206). The final authenticated version is available online at: https://doi.org/10.1007/s00574-020-00206-9