Guowu Meng

A five-variable counterexample to the Hessian conjecture, and the low-dimensional status of the Jacobian and Hessian conjectures

We exhibit an explicit integer polynomial in five variables, of total degree $14$ and with constant Hessian determinant $128$, whose gradient is not injective. Consequently its formal Legendre transform is not a polynomial, and the Hessian conjecture $\HC_5$ is false. The counterexample is obtained from the six-variabl...