Affine normal surfaces with simply-connected smooth locus

Abstract

Given a normal affine surface V defined over 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 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.

Unipotent group actions on projective varieties

“…We have a very conceptual proof of Y being smooth by using an Affine Mumford Theorem [14]. Since X is simply connected by Theorem 4.8 and the fibers of the quotient morphism are one-dimensional, Nori's theorem [35,Lemma 1.5] implies that π 1 (Y − SingY ) = 1.…”