Pull-back components of the space of foliations of codimension $\ge2$

TL;DR

This paper identifies new irreducible components in the space of holomorphic foliations of codimension at least two on projective spaces, linked to pull-back constructions via non-linear rational maps.

Contribution

It introduces a novel list of irreducible components for the space of foliations, expanding understanding of their structure through pull-back methods.

Findings

New irreducible components classified

Connection established between pull-back foliations and rational maps

Enhanced understanding of foliation moduli spaces

Abstract

We present a new list of irreducible components for the space of k-dimensional holomorphic foliations on $\mathbb P^{n}$, $n\geq3$, $k\ge2$. They are associated to pull-back of dimension one foliations on $\mathbb P^{n-k+1}$ by non-linear rational maps.