×

zbMATH — the first resource for mathematics

On the fundamental group of the complement to a maximal cuspidal plane curve. (English) Zbl 0604.14007
For integers n, \(p\geq 0\), \(n\geq 2p-1\), let C be a complex projective plane curve of degree \(2(n+p-1)\) with \(3(n+2p-2)\) cusps and \(2(n-2)(n- 3)+2p(n+p-7)\) nodes. Such maximal cuspidal curves were considered already by O. Zariski [Am. J. Math. 59, 335-358 (1937; Zbl 0016.32502)] and more recently by I. Dolgachev and A. Libgober [in Algebraic geometry, Proc. Conf. Chicago Circle 1980, Lect. Notes Math. 862, 1-25 (1981; Zbl 0475.14011)]. – Let \(H_{n,p}\) denote the fundamental group \(\pi_ 1(P^ 2\setminus C)\). Zariski has given a finite presentation of \(H_{n,p}\) for \(p=0,1\). The paper under review treats the general case by a similar method, using the Reidemeister-Schreier procedure.
Reviewer: A.Dimca

MSC:
14E20 Coverings in algebraic geometry
PDF BibTeX XML Cite
Full Text: DOI