Combinatorial computation of the motivic Poincare series

Details Combinatorial computation of the motivic Poincare series Combinatorial computation of the motivic Poincare series

2008-07-03

arxiv.org/abs/0807.0491v2

Journal of Singularities, volume 3 (2011), 48-82

Mathematics

Algebraic Geometry

43 pages

Scientific paper

10.5427/jsing.2011.3d

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.

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