论文标题
关于身份的适当性以及线性力量的一些观察：第2部分
Some observations on the properness of identity plus linear powers: part 2
论文作者
论文摘要
本文开发了我们以前关于与雅各布猜想有关的一类地图的工作的工作。该论文有两个主要部分： - 在第1部分中，我们探索了这些地图的非proper值$ s_f $（如Z. Jelonek介绍）的属性。特别是，使用这些地图的非构图的一般标准，我们表明，在“通用条件”（确切的稍后稍后）下，$ s_f $如果是非空的，则包含$ 0 $。该结果与我们以前的论文中的猜想有关。我们通过将“双集”使用到$ s_f $，特别是专为特殊类地图设计而获得的。 - 在第2部分中，我们使用在工作中获得的非专业性标准来构建与雅各布猜想的Arxiv：2002.10249中所提出的证明的反示例。 总而言之，我们提出了一些有关雅各布猜想和多项式图的义务的评论。
This paper develops our previous work on properness of a class of maps related to the Jacobian conjecture. The paper has two main parts: - In part 1, we explore properties of the set of non-proper values $S_f$ (as introduced by Z. Jelonek) of these maps. In particular, using a general criterion for non-properness of these maps, we show that under a "generic condition" (to be precise later) $S_f$ contains $0$ if it is non-empty. This result is related to a conjecture in our previous paper. We obtain this by use of a "dual set" to $S_f$, particularly designed for the special class of maps. - In part 2, we use the non-properness criteria obtained in our work to construct a counter-example to the proposed proof in arXiv:2002.10249 of the Jacobian conjecture. In the conclusion, we present some comments pertaining the Jacobian conjecture and properness of polynomial maps in general.
