{"paper":{"title":"Curvature of higher direct image sheaves and its application on negative-curvature criterion for the Weil-Petersson metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.CV","authors_text":"Xu Wang","submitted_at":"2016-07-12T08:52:17Z","abstract_excerpt":"We shall show that $q$-semipositivity of the vector bundle $E$ over a K\\\"ahler total space $\\mathcal X$ implies the Griffiths-semipositivity of the $q$-th direct image of $\\mathcal O(K_{\\mathcal X/B}\\otimes E)$. As an application, we shall give a negative-curvature criterion for the generalized Weil-Petersson metric on the base manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03265","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"}