Special metrics and stability for holomorphic bundles with global sections
type: Item
instance of: scholarly article
title: Special metrics and stability for holomorphic bundles with global sections
zbMATH Open document ID: 0697.32014
author: Steven B. Bradlow
published in: Journal of Differential Geometry
publication date: 1991-01-01T00:00:00Z
review text: We describe canonical metrics on holomorphic bundles in which there are global holomorphic sections. Such metrics are defined by the curvature of the corresponding metric connection. The constraint is in the form of a P.D.E. which looks like the Hermitian-Yang-Mills equation with an extra zeroth order term. We identify the necessary and sufficient condition for the existence of solutions to this equation. This condition is given in terms of the slopes of subsheaves of the bundle and defines a property similar to stability. We show that if a holomorphic bundle meets this stability-like criterion, then its Chern classes are constrained by an inequality similar to the Bogomolov-Gieseker inequality for stable bundles.
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 53B35
Mathematics Subject Classification ID: 55R40
zbMATH DE Number: 4142446
zbMATH Keywords: stable holomorphic bundles with global sections
zbMATH Keywords: Hermitian-Yang-Mills- Higgs metrics
zbMATH Keywords: vortex equation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214446034
OpenAlex ID: W1502762726
Wikidata QID: Q115181713
DOI: 10.4310/JDG/1214446034
description: scientific article; zbMATH DE number 4142446