Smooth contractible threefolds with hyperbolic ${\mathbb{G}}_m$-actions via ps-divisors

Abstract

The aim of this note is to give an alternative proof of a theorem of Koras and Russell, that is, a characterization of smooth contractible affine varieties endowed with a hyperbolic action of the group ${\mathbb{G}}_m\simeq {\mathbb{C}}^{\text{*}}$, using the language of polyhedral divisors developed by Altmann and Hausen as generalization of $\mathbb{Q}$-divisors.