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November 2014 Existence of approximate Hermitian-Einstein structures on semi-stable bundles
Adam Jacob
Asian J. Math. 18(5): 859-884 (November 2014).

Abstract

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.

Citation

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Adam Jacob. "Existence of approximate Hermitian-Einstein structures on semi-stable bundles." Asian J. Math. 18 (5) 859 - 884, November 2014.

Information

Published: November 2014
First available in Project Euclid: 2 December 2014

zbMATH: 1315.53079
MathSciNet: MR3287006

Subjects:
Primary: 35XX, 53XX

Rights: Copyright © 2014 International Press of Boston

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Vol.18 • No. 5 • November 2014
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