Rational real algebraic models of compact differential surfaces with circle actions

12 Apr 2019  ·  Dubouloz Adrien IMB, Petitjean Charlie ·

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...

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Algebraic Geometry