BALANCED METRICS AND CHOW STABILITY OF PROJECTIVE BUNDLES OVER RIEMANN SURFACES

In 1980, I. Morrison proved that slope stability of a vector bundle of rank 2 over a compact Riemann surface implies Chow stability of the projectivization of the bundle with respect to certain polarizations. In a previous work, we generalized Morrison's result to higher rank vector bundles over compact algebraic manifolds of arbitrary dimension that admit a constant scalar curvature metric and have a discrete automorphism group. In this article, we give a simple proof for polarizations O-PE* (d) circle times pi* L-k, where d is a positive integer, k >> 0 and the base manifold is a compact Riemann surface of genus g >= 2.