We give infinite series of groups Γ and of compact complex surfaces of general type S with fundamental group Γ such that 1) Any surface S with the same Euler number as S, and fundamental group Γ, is diffeomorphic to S. 2) The moduli space of S consists of exactly two connected components, exchanged by complex conjugation. Whence, i) On the one hand we give simple counterexamples to the DEF = DIFF question whether deformation type and diffeomorphism type coincide for algebraic surfaces. ii) On the other hand we get examples of moduli spaces without real points. iii).
