Versal deformation of transversely holomorphic flows on the boundary of strongly convex domains of $\mathbb C^n$

TL;DR

This paper constructs a versal deformation for transversely holomorphic foliations on the boundary of strongly convex domains in complex space, showing how deformations of the defining vector field induce boundary foliation deformations.

Contribution

It provides a universal deformation framework for transversely holomorphic foliations on convex domain boundaries, linking vector field deformations to boundary foliation changes.

Findings

Versal deformation of transversely holomorphic foliations established

Deformations of the holomorphic vector field induce boundary foliation deformations

Framework applies to strongly convex domains in complex spaces

Abstract

In this article, we give a versal deformation for any transversely holomorphic foliation $\mathcal{F}_0$ given by the intersection of the orbits of a holomorphic vector field $\xi$ defined on a neighborhood of the closure of a bounded strongly convex open domain $\Omega \subset\mathbb C^n$ ($n\geq2$) with smooth boundary, with its boundary $\partial \Omega$. That is, any germ of deformation of $\mathcal{F}_0$ is also obtained by intersecting the orbits of a deformation of $\xi$ with the boundary of $\Omega$.