On quadratic polynomial mappings from $\mathbb{C}^3$ to $\mathbb{C}^2$

TL;DR

This paper classifies quadratic polynomial mappings from three-dimensional complex space to two-dimensional complex space, focusing on affine and topological equivalences, advancing the understanding of polynomial map classifications.

Contribution

It provides a comprehensive classification of quadratic polynomial mappings from a73 to a72, extending previous work on mappings from a72 to a0n and aiming to classify from a73 to a073.

Findings

Classification of quadratic mappings from a73 to a72 completed

Identification of affine and topological equivalence classes

Framework established for future classifications from a73 to a073

Abstract

We classify quadratic polynomial mappings from $\mathbb{C}^3$ to $\mathbb{C}^2$ up to affine equivalence and topological equivalence. This is a part of a larger project, we have already classified mappings from $\mathbb{C}^2$ to $\mathbb{C}^n$ and inted to classify mappings from $\mathbb{C}^3$ to $\mathbb{C}^3$.