On numerically pluricanonical cyclic coverings

We investigate some properties of cyclic coverings $f\colon Y\to X$ (where $X$ is a complex surface of general type) branched along smooth curves $B\subset X$ that are numerically equivalent to a multiple of the canonical class of $X$. Our main results concern coverings of surfaces of general type with $p_g=0$ and Miyaoka–Yau surfaces. In particular, such coverings provide new examples of multi-component moduli spaces of surfaces with given Chern numbers and new examples of surfaces that are not deformation equivalent to their complex conjugates.