The Jacobi conjecture for polynomial maps

Let $f:{\mathbb{C}}^n\rightarrow{\mathbb{C}}^n$ be a polynomial map, meaning that each component $f_i:{\mathbb{C}}^n\rightarrow{\mathbb{C}}$ is polynomial. Jacobi conjecture. If the derivative $D_xf$ is invertible for every $x\in{\mathbb{C}}^n$, then $f$ is bijective and its inverse is polynomial. The conjecture is a classical problem in complex algebraic geometry and remains open in general.