Combinatorial computation of the motivic Poincaré series

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

Received: 13 September 2009. Received in revised form: 21 February 2011.

DOI: 10.5427/jsing.2011.3d

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Abstract:

We give an explicit algorithm computing the motivic generalization of the Poincaré series of a plane curve singularity introduced by A. Campillo, F. Delgado and S. Gusein-Zade. It is done in terms of the embedded resolution. 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 Heegaard-Floer knot homology constructed by P. Ozsváth and Z. Szabó. Many explicit examples are considered.

Author(s) information:

Evgeny Gorsky
Department of Mathematics
State University of New York at Stony Brook
Stony Brook, NY 11794-3651
USA
email: egorsky@math.sunysb.edu, gorsky@mccme.ru