Some properties of C* in C^2

TL;DR

This paper studies plane curves isomorphic to C* in C^2, showing that their branches at infinity can generally be separated by automorphisms and providing bounds on their self-intersection numbers.

Contribution

It demonstrates that, with one exception, branches at infinity of such curves can be separated by automorphisms of C^2 and establishes bounds on their self-intersection numbers.

Findings

Branches at infinity are separable by automorphisms in most cases.

Provides bounds for the self-intersection number of the resolution curve.

Identifies one exceptional case where separation does not occur.

Abstract

We consider plane curves isomorphic to C*. We prove that with one exception the branches at infinity can be separated by an automorphism of C^2. We also give a bound for selfintersection number of the resolution curve.