{"paper":{"title":"Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Eckart Viehweg, Kang Zuo","submitted_at":"2005-04-26T20:34:26Z","abstract_excerpt":"Given an open subset U of a projective curve Y and a smooth family f:V-->U of curves, with semi-stable reduction over Y, we show that for a sub variation of Hodge structures of rank >2 the Arakelov inequality must be strict. For families of n-folds we prove a similar result under the assumption that the (n,0) component of the Higgs bundle defines fibrewise a birational map."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504542","kind":"arxiv","version":2},"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"}