Affine normal surfaces with simply-connected smooth locus

Abstract

Given a normal affine surface V defined over \({\mathbb{C}}\), we look for algebraic and topological conditions on V which imply that V is smooth or has at most rational singularities. The surfaces under consideration are algebraic quotients \({\mathbb{C}^n/G}\) with an algebraic group action of G and topologically contractible surfaces. Theorem 3.6 can be considered as a global version of the well-known result of Mumford giving a smoothness criterion for a germ of a normal surface in terms of the local fundamental group.