Unirational elliptic surfaces in characteristic 2
type: Item
instance of: scholarly article
title: Unirational elliptic surfaces in characteristic 2
zbMATH Open document ID: 0782.14035
author: Mari Ohhira
published in: Journal of the Mathematical Society of Japan
publication date: 1994-03-02T00:00:00Z
review text: A unirational elliptic surface \(f:X\to\mathbb{P}^ 1\) defined over an algebraically closed field \(k\) of characteristic \(p\) is of base change type if there exists a surjective morphism \(g:C\to\mathbb{P}^ 1\) of curves such that \(X\times_{\mathbb{P}^ 1}C\) is a rational surface over \(k\). The author classifies completely the minimal Weierstrass normal forms of irrational unirational elliptic surfaces of base change type with sections in case \(k\) has characteristic 2; there are 21 types of them. In case char \(k>2\), \textit{T. Katsura} [Tôhoku Math. J., II. Ser. 33, 521- 553 (1981; Zbl 0466.14008)] classified such surfaces. -- As a by-product, the author shows that an irrational unirational elliptic surface of base change type with a section as a supersingular K3 surface, i.e., \(\rho(X)=b_ 2(X)\), if char \(k=2\), while this is not always the case if char \(k>2\).
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14J28
zbMATH DE Number: 218423
zbMATH Keywords: characteristic p
zbMATH Keywords: unirational elliptic surface
zbMATH Keywords: base change type
zbMATH Keywords: minimal Weierstrass normal forms
zbMATH Keywords: characteristic 2
zbMATH Keywords: supersingular K3 surface
reviewed by: M. Miyanishi
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04440709
OpenAlex ID: W1983094085
DOI: 10.2969/JMSJ/04440709
description: scientific article; zbMATH DE number 218423