Schlesinger foliation for deformations of foliations

TL;DR

This paper demonstrates that for any deformation of analytic foliations, a maximal singular foliation exists on the parameter space, ensuring the deformation's integrability along its leaves.

Contribution

It introduces the concept of Schlesinger foliation for deformations of foliations, establishing the existence of a maximal integrable foliation on the parameter space.

Findings

Existence of a maximal singular foliation for any deformation.

The maximal foliation ensures integrability along its leaves.

Provides a new geometric framework for understanding foliation deformations.

Abstract

In this article, we show that for any deformation of analytic foliations, there exists a maximal analytic singular foliation on the space of parameters along the leaves of which the deformation is integrable.