Foliations with a radial Kupka set on projective spaces

TL;DR

This paper studies a special class of holomorphic foliations on projective spaces with a radial Kupka set, proving they have rational first integrals and form an irreducible component of the foliation space.

Contribution

It establishes that foliations with a radial Kupka set on projective spaces possess rational first integrals and constitute an irreducible component of the foliation space.

Findings

Foliations with a radial Kupka set have rational first integrals.

Such foliations form an irreducible component of the space of foliations.

The study characterizes these foliations in terms of their Kupka set and Chern class.

Abstract

We consider the set $K(n,c,\rtt)$ of codimension one holomorphic foliations on $\P^n,\,\, n\geq3$, with Chern class $c$, and with a compact, connected Kupka set of radial transversal type. We will prove that foliations in this set, have a rational first integral and define an irreducible component of the space of foliations.