Poincaré series of curves on rational surface singularities (Q1772471)

Let \((C,0)\) be a reducible curve singularity, embedded into a rational surface singularity \(({\mathcal S},0)\). The Poincaré series of \(C\) is defined by the multi-index filtration on the local ring defined by orders of a function on the branches of the curve. The aim of the paper is to compute the Poincaré series of \(C\). Special properties are pointed out for curves on \({\mathbb E_8}\), namely it is shown that the Poincaré series coincides with the Alexander polynomial (in several variables) of the corresponding link.