Real Poincar\'e series of a plane divisorial valuation

Abstract

Earlier, there was computed the Poincar\'e series of a valuation or of a collection of valuations on the ring of germs of holomorphic functions in two variables. For a collection of several plane curve valuations it appeared to coincide with the Alexander polynomial of the corresponding algebraic link. Recently, the authors defined Poincar\'e series of a valuation or of a collection of valuations in the real setting. (Actually, there were defined three versions of them, however, one of them was found to be ``not computable''.) These two Poincar'e series were computed for one plane curve valuation. Here we compute them for a plane divisorial valuation.