{"paper":{"title":"The asymptotic of curvature of direct image bundle associated with higher powers of a relatively ample line bundle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Genkai Zhang, Xueyuan Wan","submitted_at":"2017-12-16T09:10:44Z","abstract_excerpt":"Let $\\pi:\\mathcal{X}\\to M$ be a holomorphic fibration with compact fibers and $L$ a relatively ample line bundle over $\\mathcal{X}$. We obtain the asymptotic of the curvature of $L^2$-metric and Qullien metric on the direct image bundle $\\pi_*(L^k\\otimes K_{\\mathcal{X}/M})$ up to the lower order terms than $k^{n-1}$ for large $k$. As an application we prove that the analytic torsion $\\tau_k(\\bar{\\partial})$ satisfies $\\partial\\bar{\\partial}\\log(\\tau_k(\\bar{\\partial}))^2=o(k^{n-1})$, where $n$ is the dimension of fibers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05922","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1712.05922/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}