Linear subspace arrangements associated with normal surface singularities

Journal of Singularities
volume 18 (2018), 464-476

Received: 27 January 2018. Accepted: 7 April 2018.

DOI: 10.5427/jsing.2018.18y

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Abstract:

Let us fix a normal surface singularity with rational homology sphere link and one of its good resolutions. It is known that each coefficient of the analytic Poincaré series associated with the multivariable divisorial filtration is the topological Euler characteristic of the complement of a certain linear subspace arrangement (determined by the divisorial filtration). In this note we construct the topological analogue valid for the multivariable topological series (zeta function) associated with the resolution graph. In this way the motivic version of this topological series can also be considered.

Keywords:

normal surface singularities, links of singularities, plumbing graphs, rational homology spheres, Poincaré series, linear subspace arrangements

Mathematical Subject Classification:

Primary. 32S05, 32S25, 32S50, 57M27 Secondary. 14Bxx, 14J80, 57R57

Author(s) information:

András Némethi
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Reáltanoda utca 13-15
H-1053, Budapest, Hungary

ELTE - University of Budapest
Dept. of Geometry
Budapest, Hungary

BCAM - Basque Center for Applied Math.
Mazarredo, 14 E48009 Bilbao
Basque Country - Spain