Geometric parametrization of valuations on a polynomial ring

TL;DR

This paper proves a conjecture relating valuations on polynomial rings to spaces of diskoids, providing a geometric parametrization that enhances understanding of valuation structures.

Contribution

It extends and proves Bengu ext{-}Lasnier's conjecture, establishing a geometric framework for valuation parametrization on polynomial rings.

Findings

Validated the conjecture through rigorous proof.

Established a correspondence between valuations and diskoids.

Enhanced geometric understanding of valuation spaces.

Abstract

We extend and prove a conjecture of Bengu\c{s}-Lasnier on the parametrization of valuations on a polynomial ring by certain spaces of diskoids.