Birational involutions of the real projective plane fall into 12 conjugacy classes, twice the number over the complex numbers, with examples where the fixed curve fails to determine the class.
Yasinsky, Automorphisms of real del Pezzo surfaces and the real plane C remona group, An- nales de l’Institut Fourier, Volume 72 (2022) no
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Birational involutions of the real projective plane
Birational involutions of the real projective plane fall into 12 conjugacy classes, twice the number over the complex numbers, with examples where the fixed curve fails to determine the class.