On quadratic polynomial mappings $f:{\mathbb{C}}^2\to {\mathbb{C}}^2$

M. Farnik, Z. Jelonek

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