A remark on Artal's paper
type: Item
instance of: scholarly article
title: A remark on Artal's paper
zbMATH Open document ID: 0894.14008
published in: Kodai Mathematical Journal
publication date: 1998-08-13T00:00:00Z
review text: This paper contains a new interpretation of an example of Zariski pairs introduced by the reviewer [\textit{E. Artal Bartolo}, J. Algebr. Geom. 3, No. 2, 223-247 (1994; Zbl 0823.14013)]. The example consists of curves with four irreducible components: a smooth cubic and three lines in general position which are tangent to inflection points of the cubic. In the reviewer's paper it was proven that the topological type of the embedding of these curves in the projective plane depends on the position of the inflection points on a line. The author proves this fact with the help of his theory about dihedral coverings. One main point of this paper is the new relationship of Zariski pairs and Mordell-Weil groups of elliptic \(K3\) surfaces.
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 949863
zbMATH Keywords: Zariski pairs
zbMATH Keywords: dihedral coverings
zbMATH Keywords: elliptic fibrations
zbMATH Keywords: topological type of the embedding
zbMATH Keywords: Mordell-Weil groups of elliptic \(K3\) surfaces
author: Hiro-O Tokunaga
reviewed by: Enrique Artal Bartolo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043600
OpenAlex ID: W2068919766
cites work: Fibre de Milnor d'un cône sur une courbe plane singulière
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DOI: 10.2996/KMJ/1138043600
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description: scientific article; zbMATH DE number 949863