${\mathbf{C}}_{+}$-actions on contractible threefolds

Shulim Kaliman, Nikolai Saveliev

Let $X$ be a smooth contractible affine algebraic threefold with a nontrivial algebraic ${\mathbf{C}}_{+}$-action on it. We show that $X$ is rational and the algebraic quotient $X//{\bf C…