Das Spektrum torsionsfreier Garben. I
type: Item
instance of: scholarly article
title: Das Spektrum torsionsfreier Garben. I
zbMATH Open document ID: 0558.14012
DOI: 10.1007/BF01174593
author: Christian Okonek
author: Heinz Spindler
published in: Manuscripta Mathematica
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155011
review text: In this paper, the authors study torsion-free sheaves of arbitrary rank on projective spaces, and in particular generalize some of R. Hartshorne's techniques and results [\textit{R. Hartshorne}, Math. Ann. 254, 121-176 (1980; Zbl 0431.14004); Invent. Math. 66, 165-190 (1982; Zbl 0519.14008)] which were originally developed for the more restricted classes of reflexive sheaves of rank 2. The study of torsion-free sheaves is important since these occur naturally in the compactifications of the moduli spaces of stable vector bundles and also as the ideal sheaves of projective varieties. The principal object of this paper is to generalize the concept of spectrum to an arbitrary torsion-free sheaf F on \({\mathbb{P}}^ 3\); this leads to inequalities for the second and third Chern classes of F similar to those which hold in the reflexive case. The authors also study the annihilators of certain cohomology classes, and hence prove under suitable conditions the existence of unstable planes for F.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 3889699
zbMATH Keywords: reflexive sheaves of rank 2
zbMATH Keywords: compactifications of the moduli spaces of stable vector bundles
zbMATH Keywords: ideal sheaves of projective varieties
zbMATH Keywords: spectrum
zbMATH Keywords: torsion-free sheaf
zbMATH Keywords: Chern classes
zbMATH Keywords: existence of unstable planes
reviewed by: P. E. Newstead
MaRDI profile type: Publication
cites work: Q4162190
cites work: Q4143433
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OpenAlex ID: W4251865469
description: scientific article; zbMATH DE number 3889699