## Equivariant Poincaré series and topology of valuations

### Summary

Summary: 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 Poincaré series determines the equivariant topology of the collection of valuations.

### Mathematics Subject Classification

14B05, 13A18, 14R20, 16W70

### Keywords/Phrases

finite group actions, Poincaré series, plane valuations, equivariant topology