{"paper":{"title":"Positivity of direct images of fiberwise Ricci-flat metrics on Calabi-Yau fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Georg Schumacher, Matthias Braun, Young-Jun Choi","submitted_at":"2015-08-03T06:44:02Z","abstract_excerpt":"Let $X$ be a K\\\"ahler manifold which is fibered over a complex manifold $Y$ such that every fiber is a Calabi-Yau manifold. Let $\\omega$ be a fixed K\\\"ahler form on $X$. By Yau's theorem, there exists a unique Ricci-flat K\\\"ahler form $\\rho\\vert_{X_y}$ for each fiber, which is cohomologous to $\\omega\\vert_{X_y}$. This family of Ricci-flat K\\\"ahler forms $\\rho\\vert_{X_y}$ induces a smooth $(1,1)$-form $\\rho$ on $X$ with a normalization condition. In this paper, we prove that the direct image of $\\rho^{n+1}$ is positive on the base $Y$. We also discuss several byproducts, among them the local tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00323","kind":"arxiv","version":5},"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"}