An example of asymptotically Chow unstable manifolds with constant scalar curvature

Abstract

Donaldson proved that if a polarized manifold $(V,L)$ has constant scalar curvature K\"ahler metrics in $c_1(L)$ and its automorphism group Aut$(M,L)$ is discrete, $(V,L)$ is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case when Aut$(V,L)$ is not discrete.