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CLASSIFICATION OF CUBIC HOMOGENEOUS POLYNOMIAL MAPS WITH JACOBIAN MATRICES OF RANK TWO
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 98 / Issue 1 / August 2018
- Published online by Cambridge University Press:
- 30 May 2018, pp. 89-101
- Print publication:
- August 2018
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- Article
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- You have access
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Let
$K$ be any field with 
$\text{char}\,K\neq 2,3$. We classify all cubic homogeneous polynomial maps 
$H$ over 
$K$ whose Jacobian matrix, 
${\mathcal{J}}H$, has 
$\text{rk}\,{\mathcal{J}}H\leq 2$. 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 
$n\neq 4$.
