Simple sheaves versus stable sheaves on algebraic surfaces
type: Item
instance of: scholarly article
title: Simple sheaves versus stable sheaves on algebraic surfaces
zbMATH Open document ID: 0735.14014
DOI: 10.1007/BF02570854
author: Zhenbo Qin
published in: Mathematische Zeitschrift
publication date: 1992-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174382
review text: It is shown that if a torsion free rank-2 sheaf is simple but not stable with respect to any polarization on a minimal algebraic surface over \(\mathbb{C}\), then it sits in a canonical nontrivial extension. As applications, we prove that every simple locally free rank-2 sheaf on a rational (ruled) surface is stable and that simple locally free rank-2 sheaves on surfaces of Kodaira dimension zero satisfy an inequality of Bogomolov-type; moreover, we essentially confirm the following conjecture of \textit{A. N. Tyurin} [see line 5, page 23 in Duke Math. J. 54, 1-26 (1987; Zbl 0631.14009)]: The irreducible component in the moduli space of simple rank-2 sheaves which contains the tangent sheaf of a \(K3\)-surface \(X\) is isogenous to the Hilbert scheme \(\text{Hilb}^{45}(X)\).
reviewed by: Zhenbo Qin
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J60
zbMATH DE Number: 4215909
zbMATH Keywords: simple sheaves
zbMATH Keywords: stable sheaves
zbMATH Keywords: torsion free rank-2 sheaf
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4215909