{"paper":{"title":"Hilbert Functions and Line Bundle Cohomology on CICY Threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Juntao Wang","submitted_at":"2026-06-20T23:55:54Z","abstract_excerpt":"Line bundle cohomology on complete intersection Calabi--Yau threefolds is an important input in string phenomenology. Previous work, based on direct extrapolation and on machine-learning analyses of finite data sets, has shown that these cohomology dimensions often admit chamber-wise polynomial descriptions on the Picard lattice. In this paper we explain this structure through the Hilbert functions associated with the non-trivial maps in the Koszul spectral sequence. Once Bott--Borel--Weil theory determines the non-vanishing ambient cohomology groups, the rank defects of the relevant Koszul ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22275","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/2606.22275/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"}