{"paper":{"title":"Castelnuovo bound for curves in projective 3-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.SG"],"primary_cat":"math.AG","authors_text":"Zhiyu Liu","submitted_at":"2024-07-29T16:40:47Z","abstract_excerpt":"The Castelnuovo bound conjecture, which is proposed by physicists, predicts an effective vanishing result for Gopakumar-Vafa invariants of Calabi-Yau 3-folds of Picard number one. Previously, it is only known for a few cases and all the proofs rely on the Bogomolov-Gieseker conjecture of Bayer-Macr\\`i-Toda.\n  In this paper, we prove the Castelnuovo bound conjecture for any Calabi-Yau 3-folds of Picard number one, up to a linear term and finitely many degree, without assuming the conjecture of Bayer-Macr\\`i-Toda. Furthermore, we prove an effective vanishing theorem for surface-counting invarian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20161","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.20161/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"}