Periodicity of the fixed locus of multiples of a divisor on a surface
type: Item
instance of: scholarly article
title: Periodicity of the fixed locus of multiples of a divisor on a surface
zbMATH Open document ID: 0803.14002
DOI: 10.1215/S0012-7094-93-07223-7
author: Steven Dale Cutkosky
author: V. Srinivas
published in: Duke Mathematical Journal
publication date: 1994-12-15T00:00:00Z
review text: Let \(D\) be an effective divisor on a nonsingular projective surface \(S\). Let \(B_ n\) be the fixed component of \(| nD |\). It is known from O. Zariski that there exists a divisor \(E\) on \(S\) such that \(B_ n - nE\) is bounded in \(n\) and also that \(B_ n - nE\) is periodic in some cases. In the paper under review the authors prove that \(B_ n - nE\) is periodic for an arbitrary effective divisor \(D\) on \(S\) if the ground field \(k\) is of characteristic 0. That this result does not hold if \(\text{char} (k) = p > 0\) is shown in a previous work by the same authors [``On a problem of Zariski on dimensions of linear systems'', Ann. Math., II. Ser. 137, 531-559 (1993)].
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14J99
zbMATH DE Number: 559005
zbMATH Keywords: periodicity of effective divisor
reviewed by: A. Del Centina
MaRDI profile type: Publication
cites work: On a problem of Zariski on dimensions of linear systems
cites work: The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface
full work available at URL: s0012-7094-93-07223-7
OpenAlex ID: W1527083798
description: scientific article; zbMATH DE number 559005