Stability of logarithmic differential one-forms

TL;DR

This paper investigates the geometric properties and stability of logarithmic differential one-forms defining codimension one foliations in projective spaces, providing new proofs and insights into their irreducible components.

Contribution

It offers a new proof of the stability of logarithmic foliations and demonstrates that their irreducible components are reduced, enhancing understanding of their geometric structure.

Findings

Logarithmic foliations are stable.

Irreducible components of the space are reduced.

Provides a new proof of stability.

Abstract

This article deals with the irreducible components of the space of codimension one foliations in a projective space defined by logarithmic forms of a certain degree. We study the geometry of the natural parametrization of the logarithmic components and we give a new proof of the stability of logarithmic foliations, obtaining also that these irreducible components are reduced.