  We study the existence of $L^2$ holomorphic sections of invariant line
bundles over Galois coverings of Zariski open sets in Moishezon manilolds. We
show that the von Neuman dimension of the space of $L^2$ holomorphic sections
is bounded below under reasonable curvature conditions. We also give criteria
for a a compact complex space with isolated singularities and some related
strongly pseudoconcave manifolds to be Moishezon. Their coverings are then
studied with the same methods. As applications we give weak Lefschetz theorems
using the Napier--Ramachandran proof of the Nori theorem.
