The moduli space of marked supersingular Enriques surfaces

We construct a moduli space of adequately marked Enriques surfaces that have a supersingular K3 cover over fields of characteristic $p\ge 3$. We show that this moduli space exists as a scheme locally of finite type over ${\mathbb{F}}_p$. Moreover, there exists a period map from this moduli space to a period scheme and we obtain a Torelli theorem for supersingular Enriques surfaces.