Coverings of locally conformally K\"ahler complex 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.