The Jacobian conjecture in dimension 3 and degree 3 (Q1805918)

The author proves the following particular case of the Jacobian conjecture: If \(k\) is an algebraically closed field of characteristic \(0\) and \(F:\mathbb A^3(k)\to\mathbb A^3(k)\) is a polynomial mapping of degree 3 with constant non-zero Jacobian, then \(F\) is an automorphism (i.e. \(F\) is bijective and \(F^{-1}\) is also polynomial).