Free C_+ -actions on C^3 are translations

Abstract

Let X' be a smooth contractible three-dimensional affine algebraic variety with a free algebraic C_+ -action on it such that S =X'// C_+ is smooth. We prove that X' is isomorphic to $S \times \C$ and the action is induced by a translation on the second factor. As a consequence we show that any free algebraic C_+ -action on C^3 is a translation in a suitable coordinate system.

12 pages