Equivariant Poincaré series and topology of valuations

The equivariant with respect to a finite group action Poincaré series of a collection of r valuations was defined earlier as a power series in r variables with the coefficients from a modification of the Burnside ring of the group. Here we show that (modulo simple exceptions) the equivariant Poincar ́e series determines the equivariant topology of the collection of valuations.Supported by the grants MTM2012-36917-C03-01 / 02 and MTM2015-65764-C3-1- P (first grant with the help of FEDER Program