Abstract
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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Partially supported by the grant MTM2007-64704 and MTM2012-36917-C03-01/02 (both grants with the help of FEDER Program). Third author was also partially supported by the Russian government grant 11.G34.31.0005, RFBR–10-01-00678, NSh–4850.2012.1 and Simons-IUM fellowship.
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Campillo, A., Delgado, F. & Gusein-Zade, S.M. Equivariant Poincaré series of filtrations and topology. Ark Mat 52, 43–59 (2014). https://doi.org/10.1007/s11512-013-0188-x
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DOI: https://doi.org/10.1007/s11512-013-0188-x