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.
Iskovskikh, Factorization of birational mappings of rational surfaces from the point of view of Mori theory , Uspekhi Mat
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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.