发表机构
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University（中国科学院数学与系统科学研究院; 湖南师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究特征零域上具有幂零雅可比矩阵的多项式映射，通过几何与推导论证给出三维情形的规范形及显式逆与驯良分解，并推广到块扩展情形，利用剩余域判据证明稳定驯良性。
AI 中文摘要
我们研究了特征为零的域上具有幂零雅可比矩阵的三变量多项式映射。所提出的分类将具有线性无关分量的映射约化为由在二次坐标处求值的一元多项式所决定的一族映射。论证的几何部分产生了分量中两个代数相关的常数线性组合。随后，一个推导论证在原始域上给出了规范形。我们得到了显式的多项式逆和驯良分解。接着，我们研究更高维的映射，其中除最后三个分量外的所有分量都依赖于三个变量。对于此类，我们给出了两个三变量块的各自规范形，并利用Berson、van den Essen和Wright的剩余域判据推导出稳定驯良性。
英文摘要
We study polynomial maps in three variables with nilpotent Jacobian over a field of characteristic zero. The proposed classification reduces maps with linearly independent components to a family determined by a univariate polynomial evaluated at a quadratic coordinate. The geometric part of the argument produces two algebraically dependent constant linear combinations of the components. A derivation argument then yields the normal form over the original field. We obtain explicit polynomial inverses and tame factorizations. We then study higher-dimensional maps in which all but the last three components depend on three variables. For this class, we give separate normal forms for the two three-variable blocks and deduce stable tameness from the residue-field criterion of Berson, van den Essen, and Wright.
Comments19 pages
