Some polynomial maps with Jacobian rank two or three

Abstract

In the paper, we first classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,z),h(x,y))$ in the case that $JH$ is nilpotent and ${°}_{z}v\le 1$. After that, we generalize the structure of $H$ to $H=(H_1(x_1,x_2,\dots ,x_n),b_3{x}_3+\cdots +b_n{x}_n+H_2^{(0)}(x_2),H_3(x_1,x_2),\dots ,H_n(x_1,x_2))$.

24 pages