Branched pull-back components of the space of codimension $2$ foliations on $\mathbb P^4$

TL;DR

This paper identifies new irreducible components of the space of codimension two holomorphic foliations on projective 4-space, constructed via pull-back by branched rational maps from foliations on projective 3-space.

Contribution

It introduces a novel list of irreducible components of the foliation space, linked to branched pull-back maps from lower-dimensional foliations.

Findings

New irreducible components of foliation space identified

Construction via branched rational maps from P^3 to P^4

Enhanced understanding of foliation moduli space structure

Abstract

We present a new list of irreducible components of the space of codimension two holomorphic foliations on $\mathbb P^{4}$. They are associated to the pull-back by branched rational maps of 1-dimensional foliations on $\mathbb P^3$ leaving $2$-dimensional planes invariant.