2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157193We prove that the moduli space of empty real Enriques surfaces (and, thus, the moduli space of compact orientable 4-dimensional Einstein manifolds whose universal covering is a K3-surface and π_1(E) = Z/2 x Z/2) is connected. The proof is based on a systematic study of real elliptic pencils and gives explicit models of all empty real Enriques surfaces.10 pages, AmS-TeX with amsppt (must be run twice)Algebraic Geometry14J28, 14P25, 53C25text