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Symmetric plane curves with nodes and cusps. (English) Zbl 0767.14011
Let \(C\) be a plane projective curve with singularities; the fundamental group \(\pi_ 1(\mathbb{P}^ 2-C)\) was studied by many authors [e.g. O. Zariski, Am. J. Math. 51, 305-328 (1929), P. Deligne in Sém. Bourbaki, 32e Année, Vol. 1979/80, Exposé 543, Lect. Notes Math. 842, 1-10 (1981; Zbl 0478.14008) and others, including the author of the present paper]. Not much is known about cuspidal curves in general.
In the paper under review the author constructs systematically plane curves with nodes and cusps, defined by symmetric polynomials and gives a lot of examples of cuspidal curves of small degree; he computes their fundamental group and the fundamental group of their complement and discusses their degenerations, obtaining in particular a new proof of some result of Zariski.
Reviewer: C.Cumino (Torino)

MSC:
14H20 Singularities of curves, local rings
14H30 Coverings of curves, fundamental group
14E20 Coverings in algebraic geometry
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