A topological characterization of \({\mathbb{C}}^ 2/G\) (Q1081653)

It is shown that an affine normal surface V which is topologically contractible and has a finite fundamental group at infinity \(\pi_ 1^{\infty}(V)\) is isomorphic to \({\mathbb{C}}^ 2/G\), where G is a small subgroup of Gl(2,\({\mathbb{C}})\), isomorphic to \(\pi_ 1^{\infty}(V)\). Examples show that none of the assumption can be removed. The proof rests on a generalization, due to Nori, of the Lefschetz hyperplane section theorem, on classical results of Kodaira concerning elliptic fibrations, and on a previous paper of the authors, proving the converse of the above result.