Rational real algebraic models of compact differential surfaces with circle actions

Adrien Dubouloz (1) , Charlie Petitjean (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Département GMP - Département de Génie Mécanique et Productique [IUT Dijon-Auxerre]

We give an algebro-geometric classification of smooth real affine algebraic surfaces endowed with an effective action of the real algebraic circle group $\mathbb{S}^1$ up to equivariant isomorphisms. As an application, we show that every compact differentiable surface endowed with an action of the circle $S^1$ admits a unique smooth rational real quasi-projective model up to $\mathbb{S}^1$-equivariant birational diffeomorphism.

Mots clés: Circle actions; torus actions; real algebraic varieties; real algebraic model; birational diffeomorphism

Domaines: Géométrie algébrique [math.AG]

Adrien Dubouloz, Charlie Petitjean. Rational real algebraic models of compact differential surfaces with circle actions. 2019. ⟨hal-02097339⟩