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We investigate Chow stability of projective bundles P(E) where E is astrictly Gieseker stable bundle over a base manifold that has constant scalarcurvature. We show that, for suitable polarisations L, the pair (P(E),L) isChow stable and give examples for which it is not asymptotically Chow stable.

A note on Chow stability of the Projectivisation of Gieseker Stable Bundles