{"paper":{"title":"Extremal K\\\"ahler metrics on projectivised vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Till Br\\\"onnle","submitted_at":"2013-01-29T20:19:27Z","abstract_excerpt":"We prove the existence of extremal, non-csc, K\\\"ahler metrics on certain unstable projectivised vector bundles $\\P (E) \\to M$ over a cscK-manifold $M$ with discrete holomorphic automorphism group, in certain adiabatic K\\\"ahler classes. In particular, the vector bundles $E \\to M$ under consideration are assumed to split as a direct sum of stable subbundles $E=E_1 \\oplus \\dots \\oplus E_s$ all having different Mumford-Takemoto-slope, e.g. $\\mu(E_1) > \\dots > \\mu(E_s)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7045","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"}