Kulikov, Vik. S. Finite presentability of the commutator subgroup of the fundamental group of the complement of a plane curve. (English. Russian original) Zbl 0935.14012 Izv. Math. 61, No. 5, 961-967 (1997); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 61, No. 5, 63-70 (1997). Let \(D\subset \mathbb{C}^{2}\) be an irreducible affine curve whose projective closure \(\overline{D}\subset \mathbb{P}^{2}\) intersects transversally the line at infinity. The author proves that the commutator subgroups: \(N=\left[ G,G\right] \) of the fundamental affine complement group \(G=\pi _{1}\left( \mathbb{C}^{2}\backslash D\right) \), and \(\overline{N}=\left[ \overline{G}, \overline{G}\right] \) of the fundamental projective complement group \( \overline{G}=\pi _{1}\left( \mathbb{P}^{2}\backslash \overline{D}\right) \) are finitely presented. Thus the situation is similar to that of fibred knots. The proof is based on author’s previous work [Vik. S. Kulikov, Russ. Acad. Sci., Izv., Math. 42, No. 1, 67-89 (1994); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 57, No. 1, 76-101 (1993; Zbl 0811.14017)], where he proved that the commutator \(N\) is finitely generated. Reviewer: A.Lipovski (Beograd) MSC: 14F35 Homotopy theory and fundamental groups in algebraic geometry 14H50 Plane and space curves 14H30 Coverings of curves, fundamental group 57M05 Fundamental group, presentations, free differential calculus 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) Keywords:fundamental group; complement of plane curve Citations:Zbl 0811.14017 PDFBibTeX XMLCite \textit{Vik. S. Kulikov}, Izv. Math. 61, No. 5, 961--967 (1997; Zbl 0935.14012); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 61, No. 5, 63--70 (1997) Full Text: DOI