Restrictions of rank-2 semistable vector bundles on surfaces in positive characteristic
type: Item
instance of: scholarly article
title: Restrictions of rank-2 semistable vector bundles on surfaces in positive characteristic
zbMATH Open document ID: 0944.14017
author: Atsushi Noma
published in: Pacific Journal of Mathematics
publication date: 1999-10-11T00:00:00Z
review text: Let \(S\) be a smooth projective surface over an algebraically closed field \(K\) with \(\text{char}(k)= p>0\), \({\mathcal O}_S(1)\) a very ample line bundle on \(S\) and \(E\) a rank-2 \({\mathcal O}_S(1)\)-semistable vector bundle on \(S\). Using ideas of \textit{L. Ein} [Math. Ann. 254, 53-72 (1980; Zbl 0431.14003)] and \textit{H. Flenner} [Comment. Math. Helv. 59, 635-650 (1984; Zbl 0599.14015)] the author finds an effective bound \(d_0\) such that if \(d\geq d_0\) the restriction \(E\mid C\) of \(E\) to a general member \(C\in|{\mathcal O}(d)|\) is semistable. In this way one gets an effective version in positive characteristic (in the case of surfaces) of a theorem of \textit{V. B. Mehta} and \textit{A. Ramanathan} [Math. Ann. 258, 213-224 (1982; Zbl 0473.14001)].
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 13A35
zbMATH DE Number: 1344320
zbMATH Keywords: semistable vector bundle
reviewed by: Iustin Coandă
MaRDI profile type: Publication
full work available at URL: pjm.1999.189.153
OpenAlex ID: W1966622024
DOI: 10.2140/PJM.1999.189.153
description: scientific article; zbMATH DE number 1344320