Moduli spaces of simple bundles and Hermitian-Einstein connections
type: Item
instance of: scholarly article
title: Moduli spaces of simple bundles and Hermitian-Einstein connections
zbMATH Open document ID: 0609.53009
DOI: 10.1007/BF01456994
author: Christian Okonek
author: M. Lübke
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164229
review text: This paper deals with moduli spaces of simple semi-connections in complex vector bundles over compact complex manifolds. By differential geometric methods we equip these spaces with the structure of a (non separated) analytic Hilbert manifold, containing the simple holomorphic structures as a finite dimensional locally Hausdorff analytic subspace. Of course we have to mention that the existence of such a structure in the space of simple holomorphic bundles is already known by the work of \textit{V. A. Norton} [Indiana Univ. Math. J. 28, 365-387 (1979; Zbl 0385.32018)], but our approach has the advantage that the moduli space of irreducible Hermitian-Einstein connections occurs as an open subset with a globally Hausdorff analytic structure.
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 58B12
zbMATH DE Number: 3986092
zbMATH Keywords: moduli spaces
zbMATH Keywords: semi-connections
zbMATH Keywords: complex vector bundles
zbMATH Keywords: complex manifolds
zbMATH Keywords: analytic Hilbert manifold
zbMATH Keywords: irreducible Hermitian-Einstein connections
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3986092