Equivalence classes of polarizations and moduli spaces of sheaves
type: Item
instance of: scholarly article
title: Equivalence classes of polarizations and moduli spaces of sheaves
zbMATH Open document ID: 0802.14005
author: Zhenbo Qin
published in: Journal of Differential Geometry
publication date: 1993-12-15T00:00:00Z
review text: The goal of the paper is to compare moduli spaces of rank-two vector- bundles slope-stable with respect to different polarizations. Let \(F\) be a rank-two vector-bundle on a projective variety \(X\), and assume \(F\) is \(L_ 1\)-stable and \(L_ 2\)-unstable: the author proves that the first Chern class of a destabilizing subsheaf satisfies certain properties. This leads naturally to the introduction of walls and chambers in the ample cone of \(X\): one salient feature is that if two polarizations \(L_ 1\), \(L_ 2\) belong to the same chamber, then \(L_ 1\)-stability is the same as \(L_ 2\)-stability. The author concentrates attention to the case \(\dim X = 2\).
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J10
zbMATH DE Number: 444710
zbMATH Keywords: moduli spaces
zbMATH Keywords: polarizations
zbMATH Keywords: destabilizing subsheaf
reviewed by: Kieran G. O'Grady
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214453682
OpenAlex ID: W1515869525
Wikidata QID: Q115180226
DOI: 10.4310/JDG/1214453682
description: scientific article; zbMATH DE number 444710