Transversely product singularities of foliations in projective spaces

TL;DR

This paper proves that in projective spaces, any transversely product component of a foliation's singular set must be a Kupka component, clarifying the structure of such singularities.

Contribution

It establishes a new link between transversely product singularities and Kupka components in holomorphic foliations on projective spaces.

Findings

Transversely product singularities are necessarily Kupka components.

The result applies to holomorphic foliations in projective spaces.

Clarifies the structure of singularities in complex foliations.

Abstract

We prove that a transversely product component of the singular set of a holomorphic foliation on $\mathbb P^n$ is necessarily a Kupka component.