Free 𝐺ₐ actions on 𝐶³

Deveney, James; Finston, David

doi:10.1090/S0002-9939-99-05412-X

Free $G_a$ actions on $C^3$
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by James K. Deveney and David R. Finston PDF

Proc. Amer. Math. Soc. 128 (2000), 31-38 Request permission

Abstract:

It has been conjectured that every free algebraic action of the additive group of complex numbers on complex affine three space is conjugate to a global translation. The main result lends support to this conjecture by showing that the morphism to the variety defined by the ring of invariants of the associated action on the coordinate ring is smooth. As a consequence, the graph morphism is an open immersion, and simple proofs of certain cases of the conjecture are obtained.

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