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arXiv · 1710.02802

Polynomial maps with nilpotent Jacobians in dimension three II

Dan Yan
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Abstract

In the paper, we first classify all polynomial maps of the form $H=(u(x,y),v(x,y,z), h(x,y))$ in the case that $JH$ is nilpotent and $(\deg_yu,\deg_yh)\leq 3$, $H(0)=0$. Then we classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,u), h(x,y))$ in the case that $JH$ is nilpotent and $(\deg v(x,y,0),\deg h)\leq 3$, $H(0)=0$. Finally, we classify polynomial maps of the form $H=(u(x,y,z),v(x,y,z), h(x,y))$ in certain conditions.

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Dan Yan. 2017-10-08. Polynomial maps with nilpotent Jacobians in dimension three II. https://arxiv.org/abs/1710.02802

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