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arXiv · 1202.4300

Equivariant Poincar\'e series of filtrations and topology

A. Campillo·F. Delgado·S. M. Gusein-Zade
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Abstract

Earlier, for an action of a finite group $G$ on a germ of an analytic variety, an equivariant $G$-Poincar\'e 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 extend the $G$-Poincar\'e 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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A. Campillo, F. Delgado, S. M. Gusein-Zade. 2012-02-20. Equivariant Poincar\'e series of filtrations and topology. https://doi.org/10.1007/s11512-013-0188-x

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