Some q-convexity properties of coverings of complex manifolds

Let C be a nowhere dense compact analytic subset of a 2-dimensional complex manifold X. A result of Napier is the construction of a neighborhood V of C such that for any covering space in which is holomorphically convex, there is a C ^∞ exhaustion function φ on which is strictly plurisubharmonic on π^-1(V) away from the compact irreducible components of . Colţoiu and Vajaitu obtained a q-convex version of this result for C a q-dimensional fiber of a proper surjective submersion X→Y. The goal of this paper is a similar version for Cprojective.