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Equivariant Poincaré series of filtrations

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Abstract

We offer a new approach to a definition of an equivariant version of the Poincaré series. This Poincaré series is defined not as a power series, but as an element of the Grothendieck ring of G-sets with an additional structure. We compute this Poincaré series for natural filtrations on the ring of germs of functions on the plane (ℂ2,0) with a finite group representation.

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Authors and Affiliations

  1. Dept. of Algebra, Geometry and Topology, Valladolid University, C/ Prado de la Magdalena s/n, 47005, Valladolid, Spain

    A. Campillo & F. Delgado

  2. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, GSP-1, 119991, Russia

    S. M. Gusein-Zade

Authors
  1. A. Campillo
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  2. F. Delgado
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  3. S. M. Gusein-Zade
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Corresponding author

Correspondence to F. Delgado.

Additional information

Partially supported by the grant MTM2007-64704 (with the help of FEDER Program). Third author is also partially supported by the grants RFBR-10-01-00678, NSh–8462.2010.1 and Visitantes distinguidos en la UCM–Grupo SANTANDER (Ay16/09).

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Campillo, A., Delgado, F. & Gusein-Zade, S.M. Equivariant Poincaré series of filtrations. Rev Mat Complut 26, 241–251 (2013). https://doi.org/10.1007/s13163-011-0077-4

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  • DOI: https://doi.org/10.1007/s13163-011-0077-4

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