On quadratic polynomial mappings $f: \Bbb C^2 \to \Bbb C^2$

TL;DR

This paper classifies all quadratic polynomial mappings from ^2 to ^2 and ^2 to ^2, showing that only finitely many exist up to linear equivalence and providing a complete list.

Contribution

It provides a complete classification of quadratic polynomial mappings from ^2 to ^2 and ^2 to ^2, enumerating all possibilities up to linear equivalence.

Findings

Finite classification of quadratic mappings over ^2 and ^2.

Explicit list of all such mappings.

Results hold over both complex and real fields.

Abstract

We show that up to linear equivalence, there is only finitely many polynomial quadratic mappings $f:\Bbb C^2\to\Bbb C^2$ and $f:\Bbb R^2\to \Bbb R^2.$ We list all possibilities.