# Rational real algebraic models of compact differential surfaces with circle actions

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02097339
Submitted on : Thursday, April 11, 2019 - 10:14:35 PM
Last modification on : Monday, June 17, 2019 - 10:30:03 AM

### Files

RealModelsDiffS1-Surf.pdf
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### Identifiers

• HAL Id : hal-02097339, version 1
• ARXIV : 1904.06082

### Citation

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

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