Some examples of Zariski pairs arising from certain elliptic K3 surfaces. II: Degtyarev's conjecture
type: Item
instance of: scholarly article
title: Some examples of Zariski pairs arising from certain elliptic K3 surfaces. II: Degtyarev's conjecture
zbMATH Open document ID: 0930.14018
DOI: 10.1007/PL00004697
published in: Mathematische Zeitschrift
publication date: 1999-09-29T00:00:00Z
review text: [For part I of this paper see Math. Z. 227, No. 3, 465-477 (1998; Zbl 0923.14012).] Two projective plane curves \(C_1, C_2\) form a Zariski pair if they have the same degree and same type of singularity but with non-isomorphic complements in the plane. An affirmative answer to Degtyarev's conjecture would imply that there is no certain Zariski pair of degree 6. Here the author among other things, disproves the conjecture by producing counterexamples. In general, it is very difficult to construct such examples due to subtlety of the difference of \(C_1, C_2\).
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14J27
zbMATH DE Number: 1336866
zbMATH Keywords: elliptic K3 surfaces
zbMATH Keywords: Zariski pair
zbMATH Keywords: singularity
zbMATH Keywords: Degtyarev's conjecture
author: Hiro-O Tokunaga
reviewed by: De-Qi Zhang
MaRDI profile type: Publication
full work available at URL: pl00004697
OpenAlex ID: W2014708401
Wikidata QID: Q123261561
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description: scientific article; zbMATH DE number 1336866