{"paper":{"title":"Balanced Metrics and Chow Stability of Projective Bundles over K\\\"ahler Manifolds II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Reza Seyyedali","submitted_at":"2011-10-25T19:30:54Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5620","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}