A new notion of Tameness

TL;DR

This paper extends the concept of tame discrete sets from complex Euclidean spaces to general complex manifolds, exploring their properties and existence in algebraic groups beyond simple cases.

Contribution

It introduces a generalized notion of tameness for discrete sets on complex manifolds and demonstrates their presence in various complex algebraic groups.

Findings

Tame discrete sets exist in complex algebraic groups other than the line or punctured line.

Basic properties of these tame sets are established.

The generalization broadens the understanding of discrete set behavior in complex geometry.

Abstract

We generalize the notion of tame discrete sets introduced by Rosay and Rudin from complex-Euclidean space to arbitrary complex manifolds and establish their basic properties. We show that complex-linear algebraic groups different from the complex line or the punctured complex line contain tame discrete sets.