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Rational Real Algebraic Models of Compact Differential Surfaces with Circle Actions

Conference paper
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Part of the Springer Proceedings in Mathematics & Statistics book series (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.

Keywords

Affine surface Real form Circle group action 

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.IMB UMR5584 CNRSUniversité Bourgogne Franche-ComtéDijonFrance
  2. 2.I.U.T. Dijon-Département GMPBoulevard Dr. PetitjeanDijonFrance

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