The moduli space of hyperbolic compact complex spaces

In this paper, we construct the moduli space of reduced hyperbolic compact complex spaces. First, we prove an infinitesimal characterization of hyperbolicity using a family of Kobayashi–Royden pseudo-metrics introduced by Venturini and as a consequence we conclude that the property of Landau holds for complex spaces. Finally, we establish this moduli space in the case of locally trivial deformations, and in a more general situation, the case of equisingular deformations.