{"paper":{"title":"Hodge classes associated to 1-parameter families of Calabi-Yau 3-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Duco van Straten, Kang Zuo, Pedro Luis del Angel, Stefan M\\\"uller-Stach","submitted_at":"2009-11-02T10:36:46Z","abstract_excerpt":"We use $L^2$-Higgs cohomology to determine the Hodge numbers of the parabolic cohomology $H^1(\\bar S, j_*\\V)$, where the local system $\\V$ arises from the third primitive cohomology of family of Calabi-Yau threefolds over a curve $\\bar S$. The method gives a way to predict the presence of algebraic 2-cycles in the total space of the family and is applied to some examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0277","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"}