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

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