Combinatorial computation of the motivic Poincare series

Abstract

We give the explicit algorithm computing the motivic generalization of the Poincare series of the plane curve singularity introduced by A. Campillo, F. Delgado and S. Gusein-Zade. It is done in terms of the embedded resolution of the curve. The result is a rational function depending of the parameter q, at q=1 it coincides with the Alexander polynomial of the corresponding link. For irreducible curves we relate this invariant to the Heegard-Floer knot homologies constructed by P. Ozsvath and Z. Szabo. Many explicit examples are considered.