Asian Journal of Mathematics

Existence of approximate Hermitian-Einstein structures on semi-stable bundles

Adam Jacob

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The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle $E$ over a compact Kähler manifold $X$. It is shown that if $E$ is semi-stable, then Donaldson’s functional is bounded from below. This implies that $E$ admits an approximate Hermitian-Einstein structure, generalizing a classic result of Kobayashi for projective manifolds to the Kähler case. As an application some basic properties of semi-stable vector bundles over compact Kähler manifolds are established, such as the fact that semi-stability is preserved under certain exterior and symmetric products.

Article information

Asian J. Math., Volume 18, Number 5 (2014), 859-884.

First available in Project Euclid: 2 December 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53XX 35XX

Approximate Hermitian-Einstein structure Donaldson functional Harder-Narasimhan filtration holomorphic vector bundle semi-stability Yang-Mills flow


Jacob, Adam. Existence of approximate Hermitian-Einstein structures on semi-stable bundles. Asian J. Math. 18 (2014), no. 5, 859--884.

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