Geodesic
Combinatorial computation of the motivic Poincaré series
Journal of Singularities, Tome 3 (2011), pp. 48-82

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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. 
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     author = {Evgeny Gorsky},
     title = {Combinatorial computation of the motivic {Poincar\'e} series},
     journal = {Journal of Singularities},
     pages = {48--82},
     publisher = {mathdoc},
     volume = {3},
     year = {2011},
     doi = {10.5427/jsing.2011.3d},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2011.3d/}
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Evgeny Gorsky. Combinatorial computation of the motivic Poincaré series. Journal of Singularities, Tome 3 (2011), pp. 48-82. doi: 10.5427/jsing.2011.3d

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