Some examples of Zariski pairs arising from certain elliptic \(K3\) surfaces
type: Item
instance of: scholarly article
title: Some examples of Zariski pairs arising from certain elliptic \(K3\) surfaces
zbMATH Open document ID: 0923.14012
DOI: 10.1007/PL00004386
published in: Mathematische Zeitschrift
publication date: 1998-06-02T00:00:00Z
review text: The author proves: There are irreducible sextics \(C_i\) (\(i=1,2\)) such that the \(C_i\) have the same singularity type but the groups \(\pi_1({\mathbb{P}}^2 \setminus C_i)\) are not isomorphic to each other. The first such example was constructed by Zariski. In general, it is hard to find such example. The author shows it by considering coverings (K3 surfaces) of \({\mathbb{P}^2}\) branched along \(C_i\). [See also part II of this paper: \textit{H. Tokunaga}, Math. Z. 230, No. 2, 389-400 (1999)].
Mathematics Subject Classification ID: 14F35
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14J28
zbMATH DE Number: 1142992
zbMATH Keywords: singularity type
zbMATH Keywords: K3 surfaces
zbMATH Keywords: fundamental group of complement of plane curves
author: Hiro-O Tokunaga
reviewed by: De-Qi Zhang
MaRDI profile type: Publication
full work available at URL: pl00004386
OpenAlex ID: W1976692112
description: scientific article; zbMATH DE number 1142992