The moduli space of hyperbolic compact complex spaces
The author constructs the moduli space of reduced hyperbolic compact complex spaces. He uses a general criterion to represent analytic functors by coarse moduli spaces. This criterion has already been used to construct the moduli space of polarized Kähler manifolds. In the first part of the paper one proves that the property of Landau holds also for complex spaces and not only for manifolds or for complex spaces with isolated singularities. After recalling the criterion allowing to represent analytic functors by coarse moduli spaces, the author proves that for any two families \(\mathcal{X}\to S\) and \(\mathcal{Y}\to S\) of reduced hyperbolic compact complex spaces parametrized by a complex space \(S\), the natural map \(\text{Bim}_S(\mathcal{X},\mathcal{Y})\to S\) is proper. Next, he considers two types of families of deformations: the first one is a family of locally trivial deformations, the second one is simultaneous resolutions of singularities.
scientific article; zbMATH DE number 5189576
scientific article