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arXiv · 1302.1589

Extension of automorphisms of rational smooth affine curves

Jérémy Blanc·Jean-Philippe Furter·Pierre-Marie Poloni
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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.

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Jérémy Blanc, Jean-Philippe Furter, Pierre-Marie Poloni. 2013-02-06. Extension of automorphisms of rational smooth affine curves. https://doi.org/10.4310/mrl.2016.v23.n1.a3

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