{"paper":{"title":"The asymptotics of the $L^2$-curvature and the second variation of analytic torsion on Teichm\\\"uller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Genkai Zhang, Xueyuan Wan","submitted_at":"2018-04-02T11:59:30Z","abstract_excerpt":"We consider the relative canonical line bundle $K_{\\mathcal{X}/\\mathcal{T}}$ and a relatively ample line bundle $(L, e^{-\\phi})$ over the total space $ \\mathcal{X}\\to \\mathcal{T}$ of fibration over the Teichm\\\"uller space by Riemann surfaces. We consider the case when the induced metric $\\sqrt{-1}\\partial\\bar{\\partial}\\phi|_{\\mathcal{X}_y}$ on $\\mathcal{X}_y$ has constant scalar curvature and we obtain the curvature asymptotics of $L^2$-metric and Quillen metric of the direct image bundle $E^k=\\pi_*(L^k+K_{\\mathcal{X}/\\mathcal{T}})$. As a consequence we prove that the second variation of analy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00464","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"}