A note on integrability and finite orbits for subgroups of Diff(C^n,0)

TL;DR

This paper extends known results on integrability and finite orbits from two-dimensional complex dynamics to higher dimensions, providing new examples of singular foliations with specific singularities and addressing open questions in the field.

Contribution

It generalizes key results on integrability and orbit finiteness for subgroups of diffeomorphisms to arbitrary dimensions and introduces new examples of singular foliations with Siegel-type singularities.

Findings

Extended results to higher dimensions for integrability and finite orbits.

Constructed examples of singular foliations with Siegel-type singularities.

Answered open question on the existence of certain singular foliations.

Abstract

In this note we extend to arbitrary dimensions a couple of results due respectively to Mattei-Moussu and to Camara-Scardua in dimension 2. We also provide examples of singular foliations having a Siegel-type singularity and answering in the negative the central question left open in the previous work of Camara-Scardua.