Linear Pullback components of the space of codimension one foliations

Abstract

The space of holomorphic foliations of codimension one and degree $d\ge 2$ in ${\mathbb{P}}^n$ ($n\ge 3$) has an irreducible component whose general element can be written as a pullback $F^{\ast }\mathcal{F}$, where $\mathcal{F}$ is a general foliation of degree $d$ in ${\mathbb{P}}^2$ and $F:{\mathbb{P}}^n⇢{\mathbb{P}}^2$ is a general rational linear map. We give a polynomial formula for the degrees of such components.

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