On the automorphism group of a certain infinite type domain in $\mathbb C^2$

TL;DR

This paper investigates the automorphism group of a specific infinite type domain in complex two-dimensional space, providing explicit descriptions of holomorphic vector fields and automorphisms at infinite type points.

Contribution

It offers a detailed analysis and explicit characterization of the automorphism group for a class of infinite type domains in ^2, which was previously not well-understood.

Findings

Explicit description of automorphism group of _P

Characterization of holomorphic vector fields tangent to the domain

Analysis of automorphisms vanishing at infinite type points

Abstract

In this article, we consider an infinite type domain $\Omega_P$ in $\mathbb C^2$. The purpose of this paper is to investigate the holomorphic vector fields tangent to an infinite type model in $\mathbb C^2$ vanishing at an infinite type point and to give an explicit description of the automorphism group of $\Omega_P$.