Balanced Metrics and Chow Stability of Projective Bundles over K?hler Manifolds II

摘要

In the previous article (Seyyedali, Duke Math. J. 153(3):573–605, 2010), we proved that slope stability of a holomorphic vector bundle E over a polarized manifold (X,L) implies Chow stability of (PE~?,O_(PE?) (1) ? π~? L~k) for k 0 if the base manifold has no nontrivial holomorphic vector field and admits a constant scalar curvature metric in the class of 2πc_1(L). In this article, using asymptotic expansions of the Bergman kernel on Sym~d E, we generalize the main theorem of Seyyedali (Duke Math. J. 153(3):573–605, 2010) to polarizations (PE~?,O_(PE*)(d)? π~? L~k) for k》0, where d is a positive integer.