Affine normal surfaces with simply-connected smooth locus

Given a normal affine surface V defined over \mathbbC{\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 \mathbbCⁿ/G{\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.