Stable bundles on hypercomplex surfaces
type: Item
instance of: scholarly article
title: Stable bundles on hypercomplex surfaces
zbMATH Open document ID: 1204.53040
author: Ruxandra Moraru
author: Misha Verbitsky
published in: Central European Journal of Mathematics
publication date: 2010-10-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0611714
review text: This article is concerned with hypercomplex manifolds, which are manifolds equipped with three complex structures \(I\), \(J\), and \(K\), which satisfy the usual quaternionic relations. The authors consider a 4-dimensional compact smooth manifold \(M\) equipped with a hypercomplex structure, and a vector bundle \(E\) over \(M\). They prove that the moduli space of anti-self-dual connections on \(E\) is hypercomplex, and admits a strong HKT metric. They also study manifolds with \((4,4)\)-supersymmetry, i.e., Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsions. Finally, they show that the moduli space of anti-self-dual connections on \(M\) is a \((4,4)\)-manifold if \(M\) is equipped with a \((4,4)\)-structure. Contents includes: Introduction, (including instanton moduli, stable holomorphic bundles, the Bismut connection, and HKT-structures); Holomorphic structures and HKT-metrics, (including \((4,4)\)-symmetry); Instanton moduli spaces, (including Hermitian-Einstein connections, stable bundles, hypercomplex structures, and HKT-metrics); and References (thirty-one items).
Mathematics Subject Classification ID: 53C26
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 14D21
zbMATH DE Number: 5797936
zbMATH Keywords: stable bundles
zbMATH Keywords: hypercomplex manifolds
zbMATH Keywords: instantons
zbMATH Keywords: generalized hyper-Kähler structures
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
OpenAlex ID: W1969627557
Wikidata QID: Q124880451
arXiv ID: math/0611714
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DOI: 10.2478/S11533-010-0006-7
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description: scientific article