# The density property for Gizatullin surfaces with reduced degenerate fibre

## TL;DR

This paper proves that Gizatullin surfaces with a specific type of $C^+$-action and reduced degenerate fibre possess the density property, and describes their automorphism groups.

## Contribution

It establishes the density property for a class of Gizatullin surfaces with certain $C^+$-actions and characterizes their automorphism groups.

## Key findings

- Gizatullin surfaces with the specified $C^+$-action have the density property.
- The identity component of the automorphism group is explicitly described.
- Surfaces with reduced degenerate fibres exhibit particular automorphism group structures.

## Abstract

All Gizatullin surfaces that admit such a $\mathbb{C}^+$-action for which the quotient is a $\mathbb{C}^1$-fibration with a reduced degenerate fibre, have the density property. We also give a description of the identity component of the group of holomorphic automorphisms of these surfaces.