On the monodromy groups of real Enriques surfaces

In this thesis we start the study of the fundamental group of the moduli space of real Enriques surfaces. The principal result is the assertion that, with one exception, any permutation of components of the half E (2) R of a real Enriques surface with a distinguished half E (1) R = Vd+2, d ≥ 1 can be realized by deformations and automorphisms. In the exceptional case ER = {V3} t {V1 t 4S} only a subgroup Z2 × Z2 ⊂ S4 can be realized.