A new class of Nilpotent Jacobians in any dimension

Álvaro Castañeda; Arno van den Essen

paper

A new class of Nilpotent Jacobians in any dimension

arXiv:1804.00584

Abstract

The classification of the nilpotent Jacobians with some structure has been an object of study because of its relationship with the Jacobian Conjecture. In this paper we classify the polynomial maps in dimension $n$ of the form $H = (u (x, y), u_{2} (x, y, x_{3}), \dots, u_{n - 1} (x, y, x_{n}), h (x, y))$ with $J H$ nilpotent. In addition we prove that the maps $X + H$ are invertible, which shows that for this kind of maps the Jacobian Conjecture is verified.