Birational involutions of the real projective plane
Algebraic Geometry
2026-04-24 v2
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 4 different classes of involutions, we discover 12 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.
Keywords
Cite
@article{arxiv.2208.00217,
title = {Birational involutions of the real projective plane},
author = {Ivan Cheltsov and Frédéric Mangolte and Egor Yasinsky and Susanna Zimmermann},
journal= {arXiv preprint arXiv:2208.00217},
year = {2026}
}
Comments
Minor corrections following referees' comments. To appear in J. Eur. Math. Soc. (JEMS)