Parametrizations of subsets of the space of valuations

TL;DR

This paper introduces new parametrization methods for subsets of the valuation space on polynomial rings, using pseudo-Cauchy sequences and approximation types, claiming improved accuracy over existing approaches.

Contribution

It presents a novel parametrization approach for valuation subsets that differs from prior methods, enhancing precision in valuation analysis.

Findings

New parametrization methods using pseudo-Cauchy sequences and approximation types.

The proposed approach is more accurate than existing methods.

Provides a detailed comparison with previous literature.

Abstract

In this paper we present different ways to parametrize subsets of the space of valuations on $K[x]$ extending a given valuation on $K$. We discuss the methods using pseudo-Cauchy sequences and approximation types. The method presented here is slightly different than the ones in the literature and we believe that our approach is more accurate.