A positive characteristic extension of a result of Del Busto on line bundles on an algebraic surface
type: Item
instance of: scholarly article
title: A positive characteristic extension of a result of Del Busto on line bundles on an algebraic surface
zbMATH Open document ID: 0910.14014
DOI: 10.1007/BF02844517
author: E. Ballico
publication date: 1998-01-11T00:00:00Z
review text: In the last few years several striking results were proven (in characteristic 0) on the behaviour of line bundles on projective varieties using very strong and interesting refinements of Mori theory. Here we will show how to give a partial extension (see theorem 1) of the main result of a paper by \textit{G. Fernández del Busto} [J. Algebr. Geom. 5, No. 3, 513-520 (1996; Zbl 0871.14006)] to positive characteristic. In our opinion this extension is not straight-forward. Theorem 1. Let \(X\) be a smooth projective surface defined over an algebraically closed field \(\mathbb{K}\); set \(p:=\text{char} (\mathbb{K})\). Fix \(A\in \text{Pic} (X)\) with \(A\) ample. If \(X\) rational assume \(p>2\). If \(\kappa (X)=2\) assume \(X\) not uniruled. If \(\kappa(X)=0,1\), assume \(p>3\). Let \(k\) be an integer \(>0\) such that \(2k> [((A\cdot (K_X+4A) +1)/A^2) + (\kappa^2 +4\kappa-2)]\). Then \(kA\) is \(\kappa\)-jet ample.
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14J60
zbMATH DE Number: 1089789
zbMATH Keywords: ampleness
zbMATH Keywords: line bundles
zbMATH Keywords: positive characteristic
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02844517
OpenAlex ID: W2090868393
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1089789