We give a bound on the number of weighted real forms of a complex variety with finite automorphism group, where the weight is the inverse of the number of automorphisms of the real form. We give another bound involving the Sylow 2-subgroup and as an application we give bounds on real forms of plane curves.

9 pages

• 14H37 - Automorphisms of curves
• 14J50 - Automorphisms of surfaces and higher-dimensional varieties
• 14P05 - Real algebraic sets