Geodesic
Plane algebraic curves in fancy balls
Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 407-420.

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Boileau and Rudolph [1] called an oriented link $L$ in the 3-sphere a \textit{$\mathbb{C}$-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 \textit{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.
Keywords: quasipositive link, $\mathbb C$-boundary
Mots-clés : Thom conjecture. 
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N. G. Kruzhilin; S. Yu. Orevkov. Plane algebraic curves in fancy balls. Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 407-420. http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a5/

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