The classification of some polynomial maps with nilpotent Jacobians

Abstract

In the paper, we first classify all polynomial maps $H$ of the following form: $H=(H_1(x_1,x_2,\dots ,x_n),H_2(x_1,x_2),H_3(x_1,x_2),\dots ,H_n(x_1,x_2))$ with $JH$ nilpotent. After that, we generalize the structure of $H$ to $H=(H_1(x_1,x_2,\dots ,x_n),H_2(x_1,x_2),H_3(x_1,x_2,H_1),\dots ,H_n(x_1,x_2,H_1))$.

Major revision with some new results. arXiv admin note: text overlap with arXiv:1710.02802, arXiv:1710.02800

References in corpus (4)

• Triangularization properties of power linear maps and the Structural Conjecture
• Polynomials with constant Hessian determinants in dimension three
• Computations of Keller maps over fields with $\frac{1}{6}$
• Quadratic homogeneous polynomial maps $H$ and Keller maps $x+H$ with $3\le \mathrm{rk}JH\le 4$