Vaisman theorem for lcK spaces

Abstract

Vaisman's theorem for locally conformally Kähler (lcK) compact manifolds states that any lcK metric on a compact complex manifold which admits a Kähler metric is, in fact, globally conformally Kähler (gcK). In this paper, we extend this theorem to compact complex spaces with singularities.

arXiv comment11 pages; v3: Corrected a few mistakes; To be published in Annali della Scuola Normale Superiore di Pisa