实1-球面在平面上多项式嵌入的唯一性
On the uniqueness of polynomial embeddings of the real 1-sphere in the plane
摘要：
本文研究了闭代数$\mathbb{C}^*$ -嵌入在$\mathbb{C}^2$中的实形式。这种嵌入的分类最近由Cassou-Nogues、Koras、Palka和Russell完成。基于它们的分类，本文证明了在代数坐标变换之前，实1-球面$\mathbb{S}^1$在仿射平面$\mathbb{R}^2$中只有一个多项式嵌入.
英文摘要：
This paper considers real forms of closed algebraic $\mathbb{C}^*$-embeddings in $\mathbb{C}^2$. The classification of such embeddings was recently completed by Cassou-Nogues, Koras, Palka and Russell. Based on their classification, this paper shows that, up to an algebraic change of coordinates, there is only one polynomial embedding of the real 1-sphere $\mathbb{S}^1$ in the affine plane $\mathbb{R}^2$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
