(2,3) torus sextics and the Albanese images of 6-fold cyclic multiple planes
type: Item
instance of: scholarly article
title: (2,3) torus sextics and the Albanese images of 6-fold cyclic multiple planes
zbMATH Open document ID: 0990.14010
published in: Kodai Mathematical Journal
publication date: 2000-02-17T00:00:00Z
review text: The author develops an approach of \textit{Vik. S. Kulikov} [Izv. Ross. Akad. Nauk, Ser. Mat. 59, No. 6, 75-94 (1995; Zbl 0939.14013)] to study the topology of cyclic multiple planes. Such planes are cyclic coverings of \({\mathbb P}^2\) ramified along a curve \(B\) and possibly along the line at infinity. In particular, for an irreducible plane sextic \(B\) with at most simple singularities the author obtains sufficient conditions under which \(B\) is a \((2,3)\) torus curve in the sense of Kulikov. As a consequence irreducible rational plane sextics with simple singularities having cyclic multiples planes of Albanese dimension 2 are described [cf. \textit{H. Tokunaga}, Proc. Am. Math. Soc. 127, No. 7, 1935-1940 (1999; Zbl 0917.14015)].
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 14J25
zbMATH DE Number: 1367786
zbMATH Keywords: plane curves
zbMATH Keywords: torus sextics
zbMATH Keywords: multiple planes
zbMATH Keywords: Albanese dimension
zbMATH Keywords: simple singularities
zbMATH Keywords: torus curve
zbMATH Keywords: rational plane sextics
author: Hiro-O Tokunaga
reviewed by: Aleksandr G. Aleksandrov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138044044
OpenAlex ID: W2015939272
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DOI: 10.2996/KMJ/1138044044
description: scientific article; zbMATH DE number 1367786