Stability of pullbacks of foliations on weighted projective spaces

TL;DR

This paper proves a stability theorem for pullback foliations on weighted projective spaces, enabling the construction of new irreducible components of foliation spaces and offering a unified proof for existing stability results.

Contribution

It introduces a stability theorem for foliations on weighted projective spaces as pullbacks, expanding the understanding of foliation moduli spaces.

Findings

Constructed many new irreducible components of foliation spaces.

Provided an alternative proof for the stability of various foliation families.

Extended stability results to foliations arising from split tangent sheaves.

Abstract

We show a stability-type theorem for foliations on projective spaces which arise as pullbacks of foliations with a split tangent sheaf on weighted projective spaces. As a consequence, we will be able to construct many irreducible components of the corresponding spaces of foliations, most of them being previously unknown. This result also provides an alternative and unified proof for the stability of other families of foliations.