# Nodal separators of holomorphic foliations

## TL;DR

This paper investigates nodal separators in singular holomorphic foliations, establishing their invariance properties and equivalence notions, with implications for understanding topological invariants of foliations.

## Contribution

It introduces intrinsic notions of equisingularity and topological equivalence for nodal separators and proves their equivalence, extending Zariski's theorem to this context.

## Key findings

- Nodal singularities and eigenvalues are topological invariants.
- Equisingularity and topological equivalence are equivalent notions for nodal separators.
- Applications to topological classification of holomorphic foliations.

## Abstract

We study a special kind of local invariant sets of singular holomorphic foliations called nodal separators. We define notions of equisingularity and topological equivalence for nodal separators as intrinsic objects and, in analogy with the celebrated theorem of Zariski for analytic curves, we prove the equivalence of these notions. We give some applications in the study of topological equivalences of holomorphic foliations. In particular, we show that the nodal singularities and its eigenvalues in the resolution of a generalized curve are topological invariants.