论文标题
飞机代数曲线
Plane algebraic curves in fancy balls
论文作者
论文摘要
Boileau and Rudolph在$ 3 $ -SPHERE中称为链接$ L $，如果可以将其作为代数曲线$ a $ a $ a $ \ bf c^2 $与光滑嵌入式$ 4 $ -BALL $ -BALL $ b $的边界的交集，则为$ \ bf c $ boundary。他们表明，某些链接不是$ \ bf c $ boundaries。我们说，如果连接$ a \ setminus b $，则$ l $是强大的$ \ bf c $ bugnary。特别是，所有准阳性链接都是强大的$ \ bf c $ boundaries。在本文中，我们提供了非质量阳性强$ \ bf c $ boundaries和non-strong $ \ bf c $ boundaries的示例。我们对（强）$ \ bf c $ boundaries进行了完整的分类，最多只有5个交叉口。
Boileau and Rudolph called a link $L$ in the $3$-sphere a $\bf C$-boundary if it can be realized as the intersection of an algebraic curve $A$ in $\bf C^2$ with the boundary of a smooth embedded $4$-ball $B$. They showed that some links are not $\bf C$-boundaries. We say that $L$ is a strong $\bf C$-boundary if $A\setminus B$ is connected. In particular, all quasipositive links are strong $\bf C$-boundaries. In this paper we give examples of non-quasipositive strong $\bf C$-boundaries and non-strong $\bf C$-boundaries. We give a complete classification of (strong) $\bf C$-boundaries with at most 5 crossings.
