Normal real affine varieties with circle actions
Annales de l'Institut Fourier, Volume 72 (2022) no. 5, pp. 1831-1857.

We provide a complete description of normal affine algebraic varieties over the real numbers endowed with an effective action of the real circle, that is, the real form of the complex multiplicative group whose real locus consists of the unitary circle in the real plane. Our approach builds on the geometrico-combinatorial description of normal affine varieties with effective actions of split tori in terms of proper polyhedral divisors on semiprojective varieties due to Altmann and Hausen.

On donne une description complète des variétés algébriques affines normales sur le corps des réels munies d’une action effective du cercle réel, c’est-à-dire la forme réelle du groupe complexe multiplicatif dont le locus réel est constitué du cercle unité dans le plan réel. Notre approche repose sur une description géométrique et combinatoire des variétés normales affines avec des actions effectives de tores en termes de diviseurs propres polyédraux sur des variétés semiprojectives dues à Altmann et Hausen.

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DOI: 10.5802/aif.3504
Classification: 14P05,  14L30
Keywords: Circle actions, torus actions, real varieties
Dubouloz, Adrien 1; Liendo, Alvaro 2

1 IMB UMR5584, CNRS, Univ. Bourgogne Franche-Comté, F-21000 Dijon, France.
2 Instituto de Matemáticas, Universidad de Talca, Casilla 721, Talca, Chile
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Dubouloz, Adrien; Liendo, Alvaro. Normal real affine varieties with  circle actions. Annales de l'Institut Fourier, Volume 72 (2022) no. 5, pp. 1831-1857. doi : 10.5802/aif.3504. https://aif.centre-mersenne.org/articles/10.5802/aif.3504/

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