Equivariant Poincaré series of filtrations and topology

Details Equivariant Poincaré series of filtrations and topology Equivariant Poincaré series of filtrations and topology

2012-02-20

arxiv.org/abs/1202.4300v1

Mathematics

Algebraic Geometry

Scientific paper

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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