A new class of Nilpotent Jacobians in any dimension

2018/04/02 by Castañeda, Álvaro, Essen, Arno van den
#14R15 14R10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/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), u₂(x,y,x₃), …, u_n-1(x,y,x_n), h(x,y)) with JH 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.

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