Normal affine surfaces properly dominated by \({\mathbb{C}}\times {\mathbb{C}}^*\) (Q1112907)

An affine variety X is said to be properly dominated by an affine variety V if there is a proper morphism \(f:\quad V\to X\) of V onto X. In this paper, we prove the following theorem: Let X be properly dominated by \({\mathbb{C}}\times {\mathbb{C}}^*\). Then X is isomorphic to \({\mathbb{C}}^ 2\), \({\mathbb{C}}\times {\mathbb{C}}^*\), \({\mathbb{C}}^ 2/G_ a\), or \({\mathbb{C}}\times {\mathbb{C}}^*/G_ b\), where \(G_ a\) (resp. \(G_ b)\) is a small finite subgroup of GL(2;\({\mathbb{C}})\) (resp. \(Aut({\mathbb{C}}\times {\mathbb{C}}^*))\).