The polar family of webs and foliations

TL;DR

This paper introduces the concept of polar curves and families for projective webs and foliations, analyzing their geometric properties and topological invariants, with results on the generic elements of these families.

Contribution

It defines polar families for webs and foliations and studies their geometric and topological properties, including the constancy of the topological embedded type for foliations.

Findings

Generic polar curves have specific geometric properties.

The topological embedded type of the generic polar is constant for foliations.

Results contribute to understanding the geometry of webs and foliations.

Abstract

We define the polar curves and the polar family associated to a projective web and obtain some results about the geometry of the generic element of this family. We also deal with the particular case of foliations and prove the constancy of the topological embedded type of the generic polar.