Universal abelian covers of superisolated singularities

The topology of a normal surface singularity does not determine the analytical invariants of its equisingularity class, but recent partial results indicated that this should be true under two restrictions, a topological one, that the link of the singularity is a rational homology sphere, and an analytical one, that the singularity is Q-Gorenstein. Neumann and Wahl conjectured that the singularity is then an abelian quotient of a complete intersection singularity, whose equations are determined in a simple way from the resolution graph [7]. Counterexamples were found by Luengo-Velasco, Melle-Hernández and Némethi [3], but they did not compute the universal abelian cover of the singularities in question. The purpose of this paper is to provide explicit examples. We give examples both of universal abelian covers and of Gorenstein singularities with integral homology sphere link, which are not complete intersections. We mention here one example with both properties, see sections 3.2. and 5.3.