Symmetric plane curves with nodes and cusps
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. \textit{O. Zariski}, Am. J. Math. 51, 305-328 (1929), \textit{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.
scientific article; zbMATH DE number 98454
scientific article