\(q\)-convexity properties of the coverings of a link singularity (Q435227)

Let \((Y,y_0)\) be the germ of a normal 2-dimensional singularity and let \(K\) be the associated link singularity. \textit{M. Colţoiu} and \textit{M. Tibăr} showed in [``Steinness of the universal covering of the complement of a 2-dimensional complex singularity'', Math. Ann. 326, 95--104 (2003; Zbl 1039.32038)] that if \(\pi_1(K)\) is an infinite group then the universal covering of \(Y\setminus\{y_0\}\) is Stein for \(Y\) small enough.NEWLINENEWLINEIn the paper under review the authors generalize this result as follows.NEWLINENEWLINELet \((Y,y_0)\) be the germ of a normal isolated singularity obtained by contracting a curve, \(\dim Y=n\geq2\), and let \(K\) be the associated link singularity. If \(\pi_1(K)\) is infinite then the universal covering space of \(Y\setminus\{y_0\}\) for \(Y\) small enough can be written as the union of \(n-1\) Stein open subsets. In particular, it is \((n-1)\)-complete.