Extensions and restrictions of holomorphic foliations

TL;DR

This paper establishes criteria for extending codimension one holomorphic foliations on projective hypersurfaces, linking their degrees, and provides examples of non-extendable foliations, advancing understanding of foliation behavior in algebraic geometry.

Contribution

It introduces an extension criterion based on degrees and explores conditions for isomorphism between foliation spaces, with concrete examples of non-extendable foliations.

Findings

Extension criterion depends on degrees of foliation and hypersurface

Isomorphism between foliation spaces under certain conditions

Examples of foliations that do not extend

Abstract

We prove an extension criterion for codimension one foliations on projective hypersurfaces based on the degree of the foliation and the degree of the hypersurface, and we ensure, in some instances, an isomorphism between the corresponding spaces of foliations. We also present some examples of foliations that do not satisfy the extension criterion and do not extend.