Real Poincar\'e series of a plane divisorial valuation

Antonio Campillo; Félix Delgado; Sabir M. Gusein-Zade

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arXiv · 2407.13455

Real Poincar\'e series of a plane divisorial valuation

Antonio Campillo·Félix Delgado·Sabir M. Gusein-Zade

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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.

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BibTeX RIS

Antonio Campillo, Félix Delgado, Sabir M. Gusein-Zade. 2024-07-18. Real Poincar\'e series of a plane divisorial valuation. https://arxiv.org/abs/2407.13455

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