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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:
 1.4e+21 Coverings in algebraic geometry
##### Keywords:
Zariski problem; fundamental group
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