ON TWIN-TRIANGULAR ADDITIVE GROUP ACTIONS ON C⁴

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 , G_a = (C, +), and σ : G_a × 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 G_a -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.

Acknowledgments