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, Rational surfaces with a pencil of rational curves and with p ositive square of the canonical class, Math
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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.