Symmetric plane curves with nodes and cusps
type: Item
instance of: scholarly article
title: Symmetric plane curves with nodes and cusps
zbMATH Open document ID: 0767.14011
author: M. Oka
published in: Journal of the Mathematical Society of Japan
publication date: 1993-01-17T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 14E20
zbMATH DE Number: 98454
zbMATH Keywords: plane curves
zbMATH Keywords: nodes
zbMATH Keywords: cusps
zbMATH Keywords: fundamental group
reviewed by: Caterina Cumino
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04430375
OpenAlex ID: W2058270116
DOI: 10.2969/JMSJ/04430375
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description: scientific article; zbMATH DE number 98454