Abstract
This paper concerns some of the conditions satisfied by additive group actions on complex affine space which can be written locally as a translation of a variable. Assume X is the affine variety C n , Ga = (C, +), and σ : Ga × X → X is the action defined by a group monomorphism G a → Aut C X. If σ is locally trivial, then the action satisfies what is termed a “GICO” condition.
It will be shown that a large class of Ga -actions on C 4, that is, fixed-point free, “twin-triangular” actions with finitely-generated rings of invariants, are at least GICO. Remaining questions are discussed.