Extension of automorphisms of rational smooth affine curves

Abstract

We provide the existence, for every complex rational smooth affine curve $\Gamma$, of a linear action of $\mathrm{Aut}(\Gamma )$ on the affine 3-dimensional space ${\mathbb{A}}^3$, together with a $\mathrm{Aut}(\Gamma )$-equivariant closed embedding of $\Gamma$ into ${\mathbb{A}}^3$. It is not possible to decrease the dimension of the target, the reason for this obstruction is also precisely described.

arXiv comment18 pages. To appear in Math. Res. Letters