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.
Fixed points of group actions and rational maps
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abstract
The aim of this note is to give simple proofs of some results of Reichstein and Youssin (math.AG/9903162) about the behaviour of fixed points of finite group actions under rational maps. Our proofs work in any characteristic. We also give a short proof of the Nishimura lemma.
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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.