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arXiv · 1803.05551

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

Michiel de Bondt·Xiaosong Sun
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Abstract

Let $K$ be any field with $\textup{char}K\neq 2,3$. We classify all cubic homogeneous polynomial maps $H$ over $K$ with $\textup{rk} JH\leq 2$. 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 $n\neq 4$.

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Michiel de Bondt, Xiaosong Sun. 2018-03-15. Classification of cubic homogeneous polynomial maps with Jacobian matrices of rank two. https://arxiv.org/abs/1803.05551

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