A note on Chow stability of the Projectivisation of Gieseker Stable   Bundles
  We investigate Chow stability of projective bundles P(E) where E is a strictly Gieseker stable bundle over a base manifold that has constant scalar curvature. We show that, for suitable polarisations L, the pair (P(E),L) is Chow stable and give examples for which it is not asymptotically Chow stable. 
Julien Keller and Julius Ross
math.DG math.AG math.CV