Deformations of pullback foliations

TL;DR

This paper investigates the stability of pullback foliations under various maps, using advanced algebraic geometry techniques, and introduces criteria for the stability of algebraic leaves within foliations.

Contribution

It develops a foliated version of Schlessinger's Theorem and applies it to establish criteria for the stability of algebraic leaves in pullback foliations.

Findings

Established a stability criterion for algebraic leaves.

Proved a foliated version of Schlessinger's Theorem.

Analyzed the behavior of pullback foliations under morphisms.

Abstract

We study the stability of pullback foliations under morphisms and rational maps via Grothendieck's Drapeaux scheme. In the local setting, a foliated version of Schlessinger's Theorem on rigidity of conical singularities was achieved. We apply these techniques to provide a criterion for the stability of algebraic leaves of a foliation.