Ample line bundles on smooth surfaces.
We give an Arakelov theoretic proof of the equality of conductor and discriminant.
We prove an analog in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.
Donaldson proved that if a polarized manifold has constant scalar curvature Kähler metrics in and its automorphism group is discrete, is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where is not discrete.