English

On real analogues of the Poincar\'e series

Algebraic Geometry 2023-06-21 v1

Abstract

There exist several equivalent equations for the Poincar\'e series of a collection of valuations on the ring of germs of functions on a complex analytic variety. We give definitions of the Poinca\'e series of a collection of valuations in the real setting (i.e., on the ring of germs of functions on a real analytic variety), compute them for the case of one curve valuation on the plane and discuss some of their properties.

Keywords

Cite

@article{arxiv.2306.10148,
  title  = {On real analogues of the Poincar\'e series},
  author = {A. Campillo and F. Delgado and S. M. Gusein-Zade},
  journal= {arXiv preprint arXiv:2306.10148},
  year   = {2023}
}