{"paper":{"title":"Counting surfaces on Calabi-Yau 4-folds I: Foundations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Hyeonjun Park, Martijn Kool, Younghan Bae","submitted_at":"2022-08-19T17:57:12Z","abstract_excerpt":"This is the first part in a series of papers on counting surfaces on Calabi-Yau 4-folds. Besides the Hilbert scheme of 2-dimensional subschemes, we introduce \\emph{two} types of moduli spaces of stable pairs. We show that all three moduli spaces are related by GIT wall-crossing and parametrize stable objects in the bounded derived category.\n  We construct \\emph{reduced} Oh-Thomas virtual cycles on the moduli spaces via Kiem-Li cosection localization and prove that they are deformation invariant along Hodge loci. As an application, we show that the variational Hodge conjecture holds for any fam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.09474","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/2208.09474/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"}