Holomorphic automorphisms of Danielewski surfaces II -- structure of the overshear group

TL;DR

This paper studies the structure of the automorphism group of Danielewski surfaces, revealing that the overshear subgroup forms a free amalgamated product, thus providing new insights into their complex geometric symmetries.

Contribution

It demonstrates that the overshear group of Danielewski surfaces is a free amalgamated product, advancing understanding of their automorphism group structure.

Findings

The overshear group is dense in the identity component of automorphisms.

The overshear group is a free amalgamated product.

Application of Nevanlinna theory to algebraic surfaces.

Abstract

We apply Nevanlinna theory for algebraic varieties to Danielewski surfaces and investigate their group of holomorphic automorphisms. Our main result states that the overshear group which is known to be dense in the identity component of the holomorphic automorphism group, is a free amalgamated product.