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arXiv · 1012.1888

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

Adam Jacob
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Abstract

The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact Kahler 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 Kahler case. As an application some basic properties of semi-stable vector bundles over compact Kahler manifolds are established, such as the fact that semi-stability is preserved under tensor product and certain exterior and symmetric products.

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Adam Jacob. 2010-12-08. Existence of approximate Hermitian-Einstein structures on semi-stable bundles. https://arxiv.org/abs/1012.1888

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