Coverings of locally conformally K\"ahler complex spaces

TL;DR

This paper investigates the properties of coverings of locally conformally K"ahler (LCK) complex spaces with singularities, establishing conditions under which coverings inherit LCK structures and generalizing previous results.

Contribution

It proves that a space is LCK if and only if its universal cover is K"ahler and shows that projections over LCK spaces with discrete fibers also admit LCK structures.

Findings

Universal cover of an LCK space is K"ahler.

Spaces projecting over LCK spaces with discrete fibers are also LCK.

Generalization of previous results on LCK spaces.

Abstract

In this paper, we study the properties of coverings of locally conformally K\"ahler (LCK) spaces with singularities. We begin by proving that a space is LCK if any only if its universal cover is K\"ahler, thereby generalizing a result from a previous paper. We then show that a complex space which projects over an LCK space with discrete fibers must also carry an LCK structure.