Existence of approximate Hermitian-Einstein structures on semi-stable bundles
Differential Geometry
2013-08-27 v3
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.
Cite
@article{arxiv.1012.1888,
title = {Existence of approximate Hermitian-Einstein structures on semi-stable bundles},
author = {Adam Jacob},
journal= {arXiv preprint arXiv:1012.1888},
year = {2013}
}
Comments
Correction of a few typos, main result unchanged. Final version to be published in Asian Journal of Mathematics. 29 pages