CLASSIFICATION OF CUBIC HOMOGENEOUS POLYNOMIAL MAPS WITH JACOBIAN MATRICES OF RANK TWO

被引：2

作者：

De Bondt, Michiel ^{[1
]}

Sun, Xiaosong ^{[2
]}

机构：

[1] Radboud Univ Nijmegen, Inst Math Astrophys & Particle Phys, Nijmegen, Netherlands

[2] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2018年 / 98卷 / 01期

关键词：

cubic homogeneous polynomial map; Jacobian conjecture; Keller map; rank-two map; tame map; TRIANGULARIZATION; AUTOMORPHISMS; CONJECTURE; TAME;

D O I：

10.1017/S0004972718000345

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be any field with char K not equal 2; 3. We classify all cubic homogeneous polynomial maps H over K whose Jacobian matrix, J H, has rk J H <= 2. In particular, we show that, for such an H, if F = x + H is a Keller map, then F is invertible and furthermore F is tame if the dimension n not equal 4.

引用

页码：89 / 101

页数：13

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