Automorphism Groups Of The Real Projective Plane With Holes And Their Conjugacy Classes Within Its Mapping Class Group

Abstract

For each integer g ≥ 2 we give the complete list of groups acting as a group of dianalytic automorphisms of a real projective plane with g holes, which, in algebraic terms, correspond to birational automorphisms of real algebraic (M − 1)-curves. We also determine those acting as the full group of automorphisms of such a surface. Furthermore, the conjugacy classes of the finite subgroups of its mapping class group are calculated.