Local Triviality of Proper Ga Actions

Regular actions of the additive group of complex numbers on complex surfaces and on complex affine space are considered. A proper action on an affine surface admits a geometric quotient which is an affine curve. A proper action on a normal quasiaffine surface is equivariantly trivial. New criteria for local and “global” triviality of proper actions on a complex affine space of arbitrary dimension are presented.