Mathematical Research Letters

Volume 23 (2016)

Number 1

Extension of automorphisms of rational smooth affine curves

Pages: 43 – 66



Jérémy Blanc (Mathematisches Institut, Universität Basel, Switzerland)

Jean-Philippe Furter (Department of Mathematics, Université de la Rochelle, France)

Pierre-Marie Poloni (Mathematisches Institut, Universität Basel, Switzerland)


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.

2010 Mathematics Subject Classification

14H45, 14R20

Accepted 17 September 2014

Published 25 May 2016