{"paper":{"title":"Deligne pairing and Quillen metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Georg Schumacher, Indranil Biswas","submitted_at":"2015-01-12T04:30:24Z","abstract_excerpt":"Let $X\\rightarrow S$ be a smooth projective surjective morphism of relative dimension $n$, where $X$ and $S$ are integral schemes over $\\mathbb C$. Let $L\\rightarrow X$ be a relatively very ample line bundle. For every sufficiently large positive integer $m$, there is a canonical isomorphism of the Deligne pairing $\\langle L ,\\cdots , L\\rangle\\rightarrow S$ with the determinant line bundle ${\\rm Det}((L- {\\mathcal O}_{X})^{\\otimes (n+1)}\\otimes L^{\\otimes m})$ \\cite{PRS}. If we fix a hermitian structure on $L$ and a relative K\\\"ahler form on $X$, then each of the line bundles ${\\rm Det}((L- {\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02539","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"}