Classification of cubic homogeneous polynomial maps with Jacobian matrices of rank two

Abstract

Let $K$ be any field with $\text{char}K\ne 2,3$. We classify all cubic homogeneous polynomial maps $H$ over $K$ with $\text{rk}JH\le 2$. In particular, we show that, for such an $H$, if $F=x+H$ is a Keller map then $F$ is invertible, and furthermore $F$ is tame if the dimension $n\ne 4$.

arXiv admin note: text overlap with arXiv:1609.09753