C-boundary links up to six crossings

An oriented link is called $\mathbb C$-boundary if it is realizable as $(\partial B,A\cap\partial B)$ where $A$ is an algebraic curve in $\mathbb C^2$ and $B$ is an embedded $4$-ball. This notion was introduced by Michel Boileau and Lee Rudolph in 1995. In a recent joint paper with N.G. Kruzhilin we gave a complete classification of $\mathbb C$-boundaries with at most 5 crossings. In the present paper a more regular method of construction of $\mathbb C$-boundaries is proposed and the classification is extended up to 6 crossings.