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

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Published 25 May 2016