The classification of some polynomial maps with nilpotent Jacobians

TL;DR

This paper classifies specific polynomial maps with nilpotent Jacobians and extends their structure to more complex forms, contributing to the understanding of polynomial map behavior in algebraic geometry.

Contribution

It provides a complete classification of polynomial maps with a particular structure and nilpotent Jacobian, and generalizes this classification to more complex polynomial maps.

Findings

Complete classification of polynomial maps with nilpotent Jacobian

Generalization to more complex polynomial map structures

Structural insights into polynomial maps in algebraic geometry

Abstract

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