On quadratic polynomial mappings from the plane into the $n$ dimensional space

TL;DR

This paper classifies all quadratic polynomial mappings from the plane to n-dimensional space over complex and real fields, showing only finitely many such mappings exist up to linear equivalence.

Contribution

It provides a complete classification of quadratic polynomial mappings from the plane into n-dimensional space, identifying all possible forms up to linear equivalence.

Findings

Finitely many quadratic polynomial mappings exist up to linear equivalence.

Complete list of all such mappings over complex and real fields.

Classification results applicable to algebraic geometry and polynomial mapping theory.

Abstract

We show that, up to linear equivalence, there are only finitely many polynomial quadratic mappings $F:\mathbb{C}^2\to\mathbb{C}^n$ and $F:\mathbb{R}^2\to\mathbb{R}^n$. We list all possibilities.