On non-Kupka points of codimension one foliations on $\mathbb{P}^3$

TL;DR

This paper investigates the structure of singularities in codimension one holomorphic foliations on projective three-space, identifying local forms of non-Kupka singularities and counting their occurrences.

Contribution

It provides a local normal form for non-Kupka components and quantifies the number of non-Kupka points within codimension two singularities.

Findings

Derived a local normal form for non-Kupka singularities

Counted the number of non-Kupka points in specific singular sets

Enhanced understanding of singularity structure in foliations on ^3

Abstract

We study the singular set of a codimension one holomorphic foliations on $\mathbb{P}^3$. We find a local normal form of a codimension two component of the singular set that is not of Kupka type. We also determined the number of non-Kupka points immersed in a codimension two component of the singular set of a codimension one foliation on $\mathbb{P}^3$.