Every locally trivial action of the additive group of complex numbers on a factorial affine variety has finitely generated ring of invariants. A criterion is given for such an action on complex four space to be conjugate to a translation. Restrictions on the nature of the singularities of the variety defined by the ring of invariants of triangular actions are noted.
"Additive group actions with finitely generated invariants." Osaka J. Math. 44 (1) 91 - 98, March 2007.