Real Poincaré series of a plane divisorial valuation

2024/07/18 by Campillo, Antonio, Delgado, Félix, Gusein-Zade, Sabir M. · 1 citation
#14B05 #16W60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.13455

Abstract

Earlier, there was computed the Poincaré 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 Poincaré 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.

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• Poincaré series of valuations on functions over a field

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