An equivariant Poincaré series of filtrations and monodromy zeta functionsстатья
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Дата последнего поиска статьи во внешних источниках: 10 октября 2015 г.
Аннотация:We define a new equivariant (with respect to a finite group action) version of the Poincaré series of a multi-index filtration as an element of the power series ring with the coefficients from a certain modification of the Burnside ring of the group. We give a formula for this Poincaré series of a collection of plane valuations in terms of a G-resolution of the collection. We show that, for filtrations on the ring of germs of functions in two variables defined by the curve valuations corresponding to the irreducible components of a plane curve singularity defined by an invariant function germ, in the majority of cases this equivariant Poincaré series determines the corresponding equivariant monodromy zeta functions defined earlier.