Holomorphic Lie Group Actions on Danielewski Surfaces

TL;DR

This paper classifies Lie group actions on Danielewski surfaces by showing they can be conjugated to simpler subgroups, advancing understanding of symmetries in complex algebraic surfaces.

Contribution

It proves that certain Lie subgroups of an infinite-dimensional topological group can be conjugated to one factor, and applies this to classify Lie group actions on Danielewski surfaces.

Findings

Lie subgroups can be conjugated to a single factor

Classification of Lie group actions on Danielewski surfaces

Application of amalgamated product structure

Abstract

We prove that any Lie subgroup $G$ (with finitely many connected components) of an infinite-dimensional topological group $\mathcal G$ which is an amalgamated product of two closed subgroups, can be conjugated to one factor. We apply this result to classify Lie group actions on Danielewski surfaces by elements of the overshear group (up to conjugation).