Is the following true ? If so, is there a quick proof of it ? (Perhaps using the uniqueness of the graded object associated to a Jordan-Holder filtration or maybe otherwise)
Suppose $ E$ is an $ \omega$ -semistable bundle with slope $ \mu$ over a compact Kahler manifold $ (X,\omega)$ . There are only finitely many (upto isomorphism) $ \omega$ -semistable subbundles of $ E$ having slope equal to $ \mu$ .
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