Séminaires : Séminaire de géométrie algébrique

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The group of birational maps of the complex plane is very large and involutions are among the first examples we meet. The question about their classification is thus very old, starting with a list by Bertini, and the full classification was achieved by Bayle-Beauville about 20 years ago. It turns out that the conjugacy classes of non-linear maps are completely determined by their fixed curve. This fails for birational involutions of the real projective plane, and in this talk I will motivate their classification. This is a collaboration with I. Cheltsov, F. Mangolte and E. Yasinsky.