On numerically pluricanonical cyclic coverings

TL;DR

This paper studies cyclic coverings of complex surfaces of general type, focusing on those branched along curves numerically equivalent to multiples of the canonical class, revealing new examples of moduli spaces and non-deformation equivalent surfaces.

Contribution

It introduces new properties and examples of cyclic coverings, especially for surfaces with p_g=0 and Miyaoka--Yau surfaces, expanding understanding of their moduli and deformation classes.

Findings

New examples of multicomponent moduli spaces with given Chern numbers

Surfaces not deformation equivalent to their complex conjugates

Insights into properties of cyclic coverings branched along specific curves

Abstract

In this article, we investigate some properties of cyclic coverings of complex surfaces of general type branched along smooth curves that are numerically equivalent to a multiple of the canonical class. The main results concern coverings of surfaces of general type with p_g=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.