Abstract
The paper gives fundamental results on the universal abelian covers of rational surface singularities. Let (X,o) be a normal complex surface singularity germ with a rational homology sphere link. Then (X,o) has the universal abelian cover (Y,o) – (X,o). It is shown that if (X,o) is rational or minimally elliptic, and if it has a star-shaped resolution graph, then (Y,o) is a complete intersection (a partial answer to the conjecture of Neumann and Wahl). A way is given to compute the multiplicity and the embedding dimension of (Y,o) from the resolution graph of (X,o) in the case when (X,o) is rational.
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