Extremal elliptic fibrations and singular \(K3\) surfaces
type: Item
instance of: scholarly article
title: Extremal elliptic fibrations and singular \(K3\) surfaces
zbMATH Open document ID: 0960.14006
author: Nguyen Khac Viet
published in: Tokyo Journal of Mathematics
publication date: 2000-06-07T00:00:00Z
review text: In this paper one considers relatively minimal fibrations \(f:X\to \mathbb{P}^1\) having a section, over an algebraically closed field of any characteristic. Firstly one recovers the classification done by \textit{U. Schmickler-Hirzebruch} [``Elliptische Flächen über \(\mathbb{P}^1\mathbb{C}\) mit drei Ausnahmefasern und die hypergeometrische Differentialgleichung'', Schriftenr. Math. Inst. Univ. Münster, n. Ser. 33 (1985; Zbl 0589.14011)] for non-trivial fibrations with at most three singular fibres in characteristic zero. Then one addresses the natural question ``For which characteristics defines the Weierstrass equation a supersingular K3 surface?'' In this respect the main result is theorem 3.4.
Mathematics Subject Classification ID: 14D06
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 1423808
zbMATH Keywords: elliptic fibration
zbMATH Keywords: Weierstrass equation
zbMATH Keywords: supersingular K3 surface
reviewed by: Nicolae Manolache
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270041447
OpenAlex ID: W2029464374
DOI: 10.3836/TJM/1270041447
description: scientific article; zbMATH DE number 1423808