Rosay-Rudin-Spaces, Tame Sets and Danielewski Surfaces

TL;DR

This paper introduces RR-spaces, a new class of complex spaces that generalize properties of tame subsets in complex Euclidean spaces, including certain algebraic groups and Danielewski surfaces.

Contribution

It defines RR-spaces and demonstrates that they encompass both complex algebraic groups and Danielewski surfaces, expanding the understanding of tame-like structures in complex geometry.

Findings

RR-spaces share properties with tame subsets in ${f C}^n$

Complex linear algebraic groups are RR-spaces

Danielewski surfaces are RR-spaces

Abstract

We introduce the notion of an ``RR-space''. (RR stands for Rosay and Rudin.) These spaces essentially share the properties of tame subsets known for ${\bf C}^n$. The class of RR-spaces contains character-free complex linear algebraic groups as well as Danielewski surfaces.