  It is shown that the singular set for the Yang-Mills flow on unstable
holomorphic vector bundles over compact Kaehler manifolds is completely
determined by the Harder-Narasimhan-Seshadri filtration of the initial
holomorphic bundle. We assign a multiplicity to irreducible top dimensional
components of the singular set of a holomorphic bundle with a filtration by
saturated subsheaves. We derive a singular Bott-Chern formula relating the
second Chern form of a smooth metric on the bundle to the Chern current of an
admissible metric on the associated graded sheaf. This is used to show that the
multiplicities of the top dimensional bubbling locus defined via the Yang-Mills
density agree with the corresponding multiplicities for the
Harder-Narasimhan-Seshadri filtration. The set theoretic equality of singular
sets is a consequence.
