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Equivariant Poincaré series of filtrations and topology

Antonio Campillo Instituto de Investigación en Matemáticas, Universidad de Valladolid Félix Delgado Instituto de Investigación en Matemáticas, Universidad de Valladolid Sabir M. Gusein-Zade Faculty of Mathematics and Mechanics, Moscow State University

K-Theory and Homology mathscidoc:1701.01021

Arkiv for Matematik, 52, (1), 43-59, 2012.5
Earlier, for an action of a finite group$G$on a germ of an analytic variety, an equivariant$G$-Poincaré series of a multi-index filtration in the ring of germs of functions on the variety was defined as an element of the Grothendieck ring of$G$-sets with an additional structure. We discuss to which extent the$G$-Poincaré series of a filtration defined by a set of curve or divisorial valuations on the ring of germs of analytic functions in two variables determines the (equivariant) topology of the curve or of the set of divisors.
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@inproceedings{antonio2012equivariant,
  title={Equivariant Poincaré series of filtrations and topology},
  author={Antonio Campillo, Félix Delgado, and Sabir M. Gusein-Zade},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637249488058},
  booktitle={Arkiv for Matematik},
  volume={52},
  number={1},
  pages={43-59},
  year={2012},
}
Antonio Campillo, Félix Delgado, and Sabir M. Gusein-Zade. Equivariant Poincaré series of filtrations and topology. 2012. Vol. 52. In Arkiv for Matematik. pp.43-59. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637249488058.
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