Plane algebraic curves in fancy balls,Izvestiya: Mathematics

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Plane algebraic curves in fancy balls
Izvestiya: Mathematics ( IF 0.8 ) Pub Date : 2021-07-08 , DOI: 10.1070/im9081
N. G. Kruzhilin ₁ , S. Yu. Orevkov ₁

Affiliation

Boileau and Rudolph [1] called an oriented link $L$ in the 3-sphere a $\mathbb{C}$ -boundary if it can be realized as the intersection of an algebraic curve $A$ in $\mathbb{C}^2$ and the boundary of a smooth embedded closed 4-ball $B$ . They showed that some links are not $\mathbb{C}$ -boundaries. We say that $L$ is a strong $\mathbb{C}$ -boundary if $A\setminus B$ is connected. In particular, all quasipositive links are strong $\mathbb{C}$ -boundaries.

In this paper we give examples of non-quasipositive strong $\mathbb{C}$ -boundaries and non-strong $\mathbb{C}$ -boundaries. We give a complete classification of (strong) $\mathbb{C}$ -boundaries with at most five crossings.

中文翻译：

花式球中的平面代数曲线

布瓦洛和鲁道夫[1]被称为定向链路 $L$ 在三维球面一个 $\mathbb{C}$ -boundary如果它可以被实现为代数曲线的交点 $A$ 在 $\mathbb{C}^2$ 和一个平滑嵌入的边界关闭4-球 $B$ 。他们表明某些链接不是 $\mathbb{C}$ 边界。如果是连通的，我们说这 $L$ 是一个强 $\mathbb{C}$ 边界 $A\set-B$ 。特别是，所有准正链接都是强 $\mathbb{C}$ 边界。

在本文中，我们给出了非拟正强 $\mathbb{C}$ 边界和非强 $\mathbb{C}$ 边界的例子。我们给出了 $\mathbb{C}$ 最多五个交叉点的（强）边界的完整分类。

更新日期：2021-07-08

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