Balanced Metrics and Chow Stability of Projective Bundles over Kähler Manifolds II

Details Balanced Metrics and Chow Stability of Projective Bundles over Kähler Manifolds II Balanced Metrics and Chow Stability of Projective Bundles over Kähler Manifolds II

2011-10-25

arxiv.org/abs/1110.5620v1

Mathematics

Differential Geometry

Scientific paper

In the previous article (\cite{S}), we proved that slope stability of a holomorphic vector bundle $E$ over a polarized manifold $(X,L)$ implies Chow stability of $(\mathbb{P}E^*,\mathcal{O}_{\mathbb{P}E^*}(1)\otimes \pi^* L^k)$ for $k \gg 0$ if the base manifold has no nontrivial holomorphic vector field and admits a constant scalar curvature metric in the class of $2\pi c_{1}(L)$. In this article using asymptotic expansions of Bergman kernel on $\textrm{Sym}^d E$, we generalize the main theorem of \cite{S} to polarizations $(\mathbb{P}E^*,\mathcal{O}_{\mathbb{P}E^*}(d)\otimes \pi^* L^k)$ for $k \gg 0$, where $d$ is a positive integer.

Affiliated with

Also associated with

No associations

Rating

Balanced Metrics and Chow Stability of Projective Bundles over Kähler Manifolds II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Balanced Metrics and Chow Stability of Projective Bundles over Kähler Manifolds II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Balanced Metrics and Chow Stability of Projective Bundles over Kähler Manifolds II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-96048