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April 2014 Equivariant Poincaré series of filtrations and topology
Antonio Campillo, Félix Delgado, Sabir M. Gusein-Zade
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Ark. Mat. 52(1): 43-59 (April 2014). DOI: 10.1007/s11512-013-0188-x

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.

Funding Statement

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.

Citation

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Antonio Campillo. Félix Delgado. Sabir M. Gusein-Zade. "Equivariant Poincaré series of filtrations and topology." Ark. Mat. 52 (1) 43 - 59, April 2014. https://doi.org/10.1007/s11512-013-0188-x

Information

Received: 4 May 2012; Revised: 13 September 2013; Published: April 2014
First available in Project Euclid: 30 January 2017

zbMATH: 1317.14006
MathSciNet: MR3175293
Digital Object Identifier: 10.1007/s11512-013-0188-x

Rights: 2013 © Institut Mittag-Leffler

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Vol.52 • No. 1 • April 2014
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