A note on singularity and non-proper value set of polynomial maps of $\mathbb{C}^2$

TL;DR

This paper investigates the relationship between singular points and non-proper value curves of polynomial maps in complex two-dimensional space using Newton-Puiseux expansions.

Contribution

It introduces a novel approach to analyze singularities and non-proper values of polynomial maps via Newton-Puiseux expansions, providing new insights into their interrelation.

Findings

Characterization of singular point sets using Newton-Puiseux expansions

Description of non-proper value curves in relation to singularities

New properties linking singularities and non-proper values

Abstract

Some properties of the relation between the singular point set and the non-proper value curve of polynomial maps of $\mathbb{C}^2$ are expressed in terms of Newton-Puiseux expansions.