Discrete equivalence of non-positive at infinity plane valuations

TL;DR

This paper investigates the structure of non-positive at infinity plane valuations, classifies their dual graphs, and provides an algorithm to construct these graphs based on valuation types.

Contribution

It introduces a classification of non-positive at infinity valuations and presents an algorithm to obtain their dual graphs, linking graph structure to valuation type.

Findings

Dual graphs are classified according to valuation type

An algorithm for constructing dual graphs is provided

The geometric behavior of these valuations is clarified

Abstract

Non-positive at infinity valuations are a class of real plane valuations which have a nice geometrical behavior. They are divided in three types. We study the dual graphs of non-positive at infinity valuations and give an algorithm for obtaining them. Moreover we compare these graphs attending the type of their corresponding valuation.