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Rational real algebraic models of compact differential surfaces with circle actions. (English) Zbl 1455.14124

Kuroda, Shigeru (ed.) et al., Polynomial rings and affine algebraic geometry. Selected papers based on the presentations at the conference, PRAAG 2018, Tokyo, Japan, February 12–16, 2018. Cham: Springer. Springer Proc. Math. Stat. 319, 109-142 (2020).
Summary: 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.
For the entire collection see [Zbl 1458.13002].

MSC:

14R20 Group actions on affine varieties
14L24 Geometric invariant theory
14B05 Singularities in algebraic geometry
14E07 Birational automorphisms, Cremona group and generalizations
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