English

Poincar\'e series of valuations on functions over a field

Algebraic Geometry 2026-05-05 v2

Abstract

For a subfield \K\K of the field \C\C of complex numbers, we consider curve and divisorial valuations on the algebra \K[[x,y]]\K[[x,y]] of formal power series in two variables with the coeficients in \K\K. We compute the semigroup Poincar\'e series and the classical Poincar\'e series of a valuation.

Keywords

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}
}