{"paper":{"title":"Polarized Hodge Structures for Clemens Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Chi Li","submitted_at":"2022-02-21T16:49:59Z","abstract_excerpt":"Let $X$ be a Calabi-Yau threefold. A conifold transition first contracts $X$ along disjoint rational curves with normal bundles of type $(-1,-1)$, and then smooth the resulting singular complex space $\\bar{X}$ to a new compact complex manifold $Y$. Such $Y$ is called a Clemens manifold and can be non-K\\\"{a}hler. We prove that any small smoothing $Y$ of $\\bar{X}$ satisfies $\\partial\\bar{\\partial}$-lemma. We also show that the resulting pure Hodge structure of weight three on $H^3(Y)$ is polarized by the cup product. These results answer some questions of R. Friedman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.10353","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.10353/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"}