Normal real affine varieties with circle actions

Adrien Dubouloz (1) , Alvaro Liendo (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Instituto de Matematica y Fisica

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

Mots clés: Circle actions; torus actions; real varieties.

Domaines: Géométrie algébrique [math.AG]

Adrien Dubouloz, Alvaro Liendo. Normal real affine varieties with circle actions. Annales de l'Institut Fourier, 2022, 72 (5), pp.1831-1857. ⟨10.5802/aif.3504⟩. ⟨hal-01909130⟩