Universal abelian covers of superisolated singularities

We give explicit examples of Gorenstein surface singularities with integral homology sphere link, which are not complete intersections. Their existence was shown by Luengo-Velasco, Melle-Hernandez and Nemethi, thereby providing counterexamples to the Universal abelian covering conjecture of Neumann and Wahl.Comment: Some examples and explanations added; updated version. 23 page

The embedding dimension of weighted homogeneous surface singularities

We analyze the embedding dimension of a normal weighted homogeneous surface singularity, and more generally, the Poincar\'e series of the minimal set of generators of the graded algebra of regular functions, provided that the link of the germs is a rational homology sphere. In the case of several sub-families we provide explicit formulas in terms of the Seifert invariants (generalizing results of Wagreich and VanDyke), and we also provide key examples showing that, in general, these invariants are not topological. We extend the discussion to the case of splice--quotient singularities with star--shaped graph as well.Comment: 25 pages, Revised version, to appear in Journal of Topolog