JournalsjemsVol. 28, No. 8pp. 3653–3711

Birational involutions of the real projective plane

  • Ivan Cheltsov

    University of Edinburgh, UK

  • Frédéric Mangolte

    Aix-Marseille Université, France

  • Egor Yasinsky

    Université de Bordeaux, Talence, France

  • Susanna Zimmermann

    Université Paris-Saclay, Orsay Ville, France
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Abstract

We classify birational involutions of the real projective plane up to conjugation. In contrast with an analogous classification over the complex numbers (due to E. Bertini, G. Castelnuovo, F. Enriques, L. Bayle and A. Beauville), which includes four different classes of involutions, we discover different classes over the reals, and provide many examples when the fixed curve of an involution does not determine its conjugacy class in the real plane Cremona group.

Cite this article

Ivan Cheltsov, Frédéric Mangolte, Egor Yasinsky, Susanna Zimmermann, Birational involutions of the real projective plane. J. Eur. Math. Soc. 28 (2026), no. 8, pp. 3653–3711

DOI 10.4171/JEMS/1537