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On topological approaches to the Jacobian conjecture in ℂn
Proceedings of the Edinburgh Mathematical Society ( IF 0.7 ) Pub Date : 2020-05-07 , DOI: 10.1017/s0013091520000061 Francisco Braun , Luis Renato Gonçalves Dias , Jean Venato-Santos
Proceedings of the Edinburgh Mathematical Society ( IF 0.7 ) Pub Date : 2020-05-07 , DOI: 10.1017/s0013091520000061 Francisco Braun , Luis Renato Gonçalves Dias , Jean Venato-Santos
We obtain a new theorem for the non-properness set $S_f$ of a non-singular polynomial mapping $f:\mathbb C^n \to \mathbb C^n$ . In particular, our result shows that if f is a counterexample to the Jacobian conjecture, then $S_f\cap Z \neq \emptyset $ , for every hypersurface Z dominated by $\mathbb C^{n-1}$ on which some non-singular polynomial $h: \mathbb C^{n}\to \mathbb C$ is constant. Also, we present topological approaches to the Jacobian conjecture in $\mathbb C^n$ . As applications, we extend bidimensional results of Rabier, Lê and Weber to higher dimensions.
中文翻译:
关于ℂn中雅可比猜想的拓扑方法
我们得到了一个关于非属性集的新定理$S_f$ 非奇异多项式映射的$f:\mathbb C^n \to \mathbb C^n$ . 特别是,我们的结果表明,如果F 是雅可比猜想的反例,则$S_f\cap Z \neq \emptyset $ , 对于每个超曲面Z 被)占据$\mathbb C^{n-1}$ 其中一些非奇异多项式$h: \mathbb C^{n}\to \mathbb C$ 是恒定的。此外,我们提出了雅可比猜想的拓扑方法$\mathbb C^n$ . 作为应用,我们将 Rabier、Lê 和 Weber 的二维结果扩展到更高维度。
更新日期:2020-05-07
中文翻译:
关于ℂn中雅可比猜想的拓扑方法
我们得到了一个关于非属性集的新定理