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.
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页码：89 / 101
页数：13
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