{"paper":{"title":"Balanced metrics on homogeneous vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Roberto Mossa","submitted_at":"2011-01-16T16:38:14Z","abstract_excerpt":"Let $E\\rightarrow M$ be a holomorphic vector bundle over a compact Kaehler manifold $(M, \\omega)$ and let $E=E_1\\oplus... \\oplus E_m\\rightarrow M$ be its decomposition into irreducible factors. Suppose that each $E_j$ admits a $\\omega$-balanced metric in Donaldson-Wang terminology. In this paper we prove that $E$ admits a unique $\\omega$-balanced metric if and only if $\\frac{r_j}{N_j}=\\frac{r_k}{N_k}$ for all $j, k=1, ..., m$, where $r_j$ denotes the rank of $E_j$ and $N_j=\\dim H^0(M, E_j)$. We apply our result to the case of homogeneous vector bundles over a rational homogeneous variety $(M, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3078","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"}