On numerically pluricanonical cyclic coverings

International audienceIn this article, we investigate some properties of cyclic coverings f : Y → X of complex surfaces of general type X branched along smooth curves B ⊂ X that are numerically equivalent to a multiple of the canonical class of X. The main results concern coverings of surfaces of general type with pg = 0 and Miyaoka–Yau surfaces; in particular, they provide new examples of multicomponent moduli spaces of surfaces with given Chern numbers as well as new examples of surfaces that are not deformation equivalent to their complex conjugates