{"paper":{"title":"Curvature of higher direct image sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Georg Schumacher, Thomas Geiger","submitted_at":"2015-01-28T11:39:33Z","abstract_excerpt":"Given a family $(F,h) \\to X \\times S$ of Hermite-Einstein bundles on a compact K\\\"ahler manifold $(X,g)$ we consider the higher direct image sheaves $R^q p_* \\mathcal{O}(F)$ on $S$, where $p: X \\times S \\to S$ is the projection. On the complement of an analytic subset these sheaves are locally free and carry a natural metric, induced by the $L_2$ inner product of harmonic forms on the fibers. We compute the curvature of this metric which has a simpler form for families with fixed determinant and families of endomorphism bundles. Furthermore, we discuss the metric for moduli spaces of stable ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07070","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"}