{"paper":{"title":"The Nakano vanishing theorem and a vanishing theorem of Demailly-Nadel type for holomorphic vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.CV","authors_text":"Hossein Raufi","submitted_at":"2012-12-18T16:38:43Z","abstract_excerpt":"We prove the classical Nakano vanishing theorem with H\\\"ormander $L^2$-estimates on a compact K\\\"ahler manifold using Siu's so called $\\partial\\dbar$-Bochner-Kodaira method, thereby avoiding the K\\\"ahler identities completely. We then introduce singular hermitian metrics on holomorphic vector bundles, and proceed to prove a vanishing theorem of Demailly-Nadel type for these in the special case where the base manifold is a Riemann surface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4417","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"}