Abstract:
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.
Keywords:numerically pluricanonical cyclic coverings of surfaces,
irreducible components of moduli spaces of surfaces.