A new class of Nilpotent Jacobians in any dimension

Álvaro Castañeda; Arno van den Essen

A new class of Nilpotent Jacobians in any dimension

Algebraic Geometry 2018-09-07 v2

Authors: Álvaro Castañeda , Arno van den Essen

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 $H = (u(x,y), u_2(x,y,x_3), \ldots, u_{n-1}(x,y,x_n), h(x,y))$ 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.

Keywords

nilpotent jacobians polynomial maps jacobian conjecture invertible maps

Cite

@article{arxiv.1804.00584,
  title  = {A new class of Nilpotent Jacobians in any dimension},
  author = {Álvaro Castañeda and Arno van den Essen},
  journal= {arXiv preprint arXiv:1804.00584},
  year   = {2018}
}

A new class of Nilpotent Jacobians in any dimension

Abstract

Keywords

Cite

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