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.
Revised:
Accepted:
Published online:
Keywords: Circle actions, torus actions, real varieties
Mot clés : actions du cercle, action du tore, variétées réelles
@article{AIF_2022__72_5_1831_0, author = {Dubouloz, Adrien and Liendo, Alvaro}, title = {Normal real affine varieties with circle actions}, journal = {Annales de l'Institut Fourier}, pages = {1831--1857}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {5}, year = {2022}, doi = {10.5802/aif.3504}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.3504/} }
TY - JOUR AU - Dubouloz, Adrien AU - Liendo, Alvaro TI - Normal real affine varieties with circle actions JO - Annales de l'Institut Fourier PY - 2022 SP - 1831 EP - 1857 VL - 72 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3504/ DO - 10.5802/aif.3504 LA - en ID - AIF_2022__72_5_1831_0 ER -
%0 Journal Article %A Dubouloz, Adrien %A Liendo, Alvaro %T Normal real affine varieties with circle actions %J Annales de l'Institut Fourier %D 2022 %P 1831-1857 %V 72 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3504/ %R 10.5802/aif.3504 %G en %F AIF_2022__72_5_1831_0
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. http://archive.numdam.org/articles/10.5802/aif.3504/
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