The limit of the Yang-Mills flow on semi-stable bundles
Abstract
By the work of Hong and Tian it is known that given a holomorphic vector bundle E over a compact Kahler manifold X, the Yang-Mills flow converges away from an analytic singular set. If E is semi-stable, then the limiting metric is Hermitian-Einstein and will decompose the limiting bundle into a direct sum of stable bundles. Bando and Siu prove this limiting bundle can be extended to a reflexive sheaf E' on all of X. In this paper, we construct an isomorphism between E' and the double dual of the stable quotients of the graded Seshadri filtration of E.
Keywords
Cite
@article{arxiv.1104.4767,
title = {The limit of the Yang-Mills flow on semi-stable bundles},
author = {Adam Jacob},
journal= {arXiv preprint arXiv:1104.4767},
year = {2013}
}
Comments
Correction of a few typos to address referee's comments. Contains a new proof of Proposition 2 to address an error pointed out by T. Collins and the referee. Main results unchanged. Final version to appear in Crelle's Journal. 13 pages