Free C+ -actions on C3 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 × and the action is induced by a translation on the second factor. As a consequence we show that any free algebraic C+ -action on C3 is a translation in a suitable coordinate system.
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