3 papers
math.AG2025
Poincaré series of valuations on functions over a field
Antonio Campillo, Felix Delgado, Sabir Gusein-Zade
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the co…
math.AG2024
Real Poincaré series of a plane divisorial valuation
Antonio Campillo, Félix Delgado, Sabir M. Gusein-Zade
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…
math.AG2023
On real analogues of the Poincaré series
A. Campillo, F. Delgado, S. M. Gusein-Zade
There exist several equivalent equations for the Poincaré series of a collection of valuations on the ring of germs of functions on a complex analytic variety. We give definitions…