Functional Analysis and Its Applications

, Volume 42, Issue 2, pp 83–88 | Cite as

Universal Abelian covers of rational surface singularities and multi-index filtrations

  • S. M. Gusein-Zade
  • F. Delgado
  • A. Campillo


In previous papers, the authors computed the Poincaré series of some (multi-index) filtrations on the ring of germs of functions on a rational surface singularity. These Poincaré series were expressed as the integer parts of certain fractional power series, whose interpretation was not given. In this paper, we show that, up to a simple change of variables, these fractional power series are reductions of the equivariant Poincaré series for filtrations on the ring of germs of functions on the universal Abelian cover of the surface. We compute these equivariant Poincaré series.

Key words

universal Abelian cover rational surface singularity Poincaré series 


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Department of Mathematics and MechanicsMoscow State UniversityRussia
  2. 2.Dept. of Algebra, Geometry and TopologyUniversity of ValladolidSpain

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