论文标题

一种统一的方法,以三个空间的线嵌入

A unified approach to embeddings of a line in 3-space

论文作者

Lewis, Drew

论文摘要

虽然是否可以整理仿射$ 3 $空间的仿射线的每一个封闭嵌入的总体嵌入,但已经通过几种不同的方式证明了一些部分结果。我们提供了一种新的方法,即(强烈)剩余的坐标,使我们能够提供所有已知部分结果的新证明,尤其是概括了Bhatwadekar-Roy和Kuroda的结果,以$(T^n,t^m,t^l+t)的形式嵌入。

While the general question of whether every closed embedding of an affine line in affine $3$-space can be rectified remains open, there have been several partial results proved by several different means. We provide a new approach, namely constructing (strongly) residual coordinates, that allows us to give new proofs of all known partial results, and in particular generalize the results of Bhatwadekar-Roy and Kuroda on embeddings of the form $(t^n,t^m,t^l+t)$.

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