Abstract
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.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 42, No. 2, pp. 3–10, 2008
Original Russian Text Copyright © by S. M. Gusein-Zade, F. Delgado, and A. Campillo
The research of the first author was supported in part by grants RFBR-007-00593, INTAS-05-7805, NWO-RFBR 047.011.2004.026, and RFBR-JSPS 06-01-91063. The last two authors were supported in part by grant MTM2007-64704.
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Gusein-Zade, S.M., Delgado, F. & Campillo, A. Universal Abelian covers of rational surface singularities and multi-index filtrations. Funct Anal Its Appl 42, 83–88 (2008). https://doi.org/10.1007/s10688-008-0013-7
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DOI: https://doi.org/10.1007/s10688-008-0013-7