Poincar\'e series of valuations on functions over a field
Algebraic Geometry
2026-05-05 v2
Abstract
For a subfield of the field of complex numbers, we consider curve and divisorial valuations on the algebra of formal power series in two variables with the coeficients in . We compute the semigroup Poincar\'e series and the classical Poincar\'e series of a valuation.
Cite
@article{arxiv.2506.02693,
title = {Poincar\'e series of valuations on functions over a field},
author = {Antonio Campillo and Felix Delgado and Sabir Gusein-Zade},
journal= {arXiv preprint arXiv:2506.02693},
year = {2026}
}