The limit of the Yang-Mills flow on semi-stable bundles

Details The limit of the Yang-Mills flow on semi-stable bundles The limit of the Yang-Mills flow on semi-stable bundles

2011-04-25

arxiv.org/abs/1104.4767v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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.

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