Puiseux Parametric Equations via the Amoeba of the Discriminant

TL;DR

This paper introduces a method to obtain Puiseux parametrizations of algebraic varieties within specific Reinhardt domains, utilizing the amoeba of hypersurfaces related to the discriminant locus of finite projections.

Contribution

It presents a novel approach connecting amoebas of hypersurfaces to Puiseux parametrizations, expanding tools for analyzing algebraic varieties.

Findings

Puiseux parametrizations are obtained on Reinhardt domains.

Amoebas of hypersurfaces are used to define these domains.

The method relates discriminant loci to parametrization techniques.

Abstract

Given an algebraic variety we get Puiseux type parametrizations on suitable Reinhardt domains. These domains are defined using the amoeba of hypersurfaces containing the discriminant locus of a finite projection of the variety.