Moduli of Hermite-Einstein vector bundles
type: Item
instance of: scholarly article
title: Moduli of Hermite-Einstein vector bundles
zbMATH Open document ID: 0602.53042
DOI: 10.1007/BF01161608
author: Hong-Jong Kim
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183682
review text: On a compact Kähler manifold M, it is shown that the moduli space of Hermite-Einstein vector bundles is a complex manifold under a suitable cohomological assumption, namely, \(H^ 2(M, sl \epsilon)=0\), where sl \(\epsilon\) is the bundle of trace-free endomorphisms of a holomorphic vector bundle \(\epsilon\) over M. The tangent space of the moduli space at the point [\(\epsilon\) ] is isomorphic to the sheaf-cohomology group \(H^ 1(M, End \epsilon)\). Similar argument applies to show that the moduli space of simple holomorphic vector bundles is a (non-Hausdorff) complex manifold under the same cohomological assumption. As a corollary, we obtain that the moduli space of stable bundles on a nonsingular irreducible projective algebraic surface with nonnegative total scalar curvature is a Kähler manifold.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 3971675
zbMATH Keywords: Kähler manifold
zbMATH Keywords: moduli space
zbMATH Keywords: Hermite-Einstein vector bundles
zbMATH Keywords: holomorphic vector bundles
zbMATH Keywords: projective algebraic surface
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3971675