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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Dubouloz, A., Petitjean, C. (2020). Rational Real Algebraic Models of Compact Differential Surfaces with Circle Actions. In: Kuroda, S., Onoda, N., Freudenburg, G. (eds) Polynomial Rings and Affine Algebraic Geometry. PRAAG 2018. Springer Proceedings in Mathematics & Statistics, vol 319. Springer, Cham. https://doi.org/10.1007/978-3-030-42136-6_4
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DOI: https://doi.org/10.1007/978-3-030-42136-6_4
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