{"paper":{"title":"On the $L^2$-$\\overline{\\partial}$-cohomology of certain complete K\\\"ahler metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Francesco Bei, Paolo Piazza","submitted_at":"2015-09-21T10:13:36Z","abstract_excerpt":"Let $V$ be a compact and irreducible complex space of complex dimension $v$ whose regular part is endowed with a complete Hermitian metric $h$. Let $\\pi:M\\rightarrow V$ be a resolution of $V$. Under suitable assumptions on $h$ we prove that $$H^{v,q}_{2,\\overline{\\partial}}(\\operatorname{reg}(V),g)\\cong H^{v,q}_{\\overline{\\partial}}(M),\\ q=0,...,v.$$ Then we show that the previous isomorphism applies to the case of Saper-type K\\\"ahler metrics and to the case of complete K\\\"ahler metrics with finite volume and pinched negative sectional curvatures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06174","kind":"arxiv","version":3},"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"}