  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. We generalized Morrison's
result to higher rank vector bundles over compact algebraic manifolds of
arbitrary dimension that admit constant scalar curvature metric and have
discrete automorphism group. In this article, we give a simple proof for
polarizations $\mathcal{O}_{\mathbb{P}E^*}(d)\otimes \pi^* L^k$, where $d$ is a
positive integer, $k \gg 0$ and the base manifold is a compact Riemann surface
of genus $g \geq 2$.
