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Rational Real Algebraic Models of Compact Differential Surfaces with Circle Actions

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Polynomial Rings and Affine Algebraic Geometry (PRAAG 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 319))

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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Author information

Authors and Affiliations

  1. IMB UMR5584 CNRS, Université Bourgogne Franche-Comté, 21000, Dijon, France

    Adrien Dubouloz

  2. I.U.T. Dijon-Département GMP, Boulevard Dr. Petitjean, 21078, Dijon, France

    Charlie Petitjean

Authors
  1. Adrien Dubouloz
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  2. Charlie Petitjean
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Corresponding author

Correspondence to Adrien Dubouloz .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Tokyo Metropolitan University, Hachioji, Tokyo, Japan

    Shigeru Kuroda

  2. Faculty of Applied Physics, University of Fukui, Fukui, Japan

    Nobuharu Onoda

  3. Department of Mathematics, Western Michigan University, Kalamazoo, MI, USA

    Gene Freudenburg

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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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