{"paper":{"title":"Effective positivity of Hodge bundles and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giulio Codogni, Luca Tasin, Zsolt Patakfalvi","submitted_at":"2025-06-12T09:23:36Z","abstract_excerpt":"We prove new boundedness results across different areas of algebraic geometry, stemming from a unifying technical starting point: bounding the integer $q > 0$ such that the $q$-th Hodge bundle becomes (semi-)positive for families of stable varieties. This result allows us to show that for stable families $f: X \\to T$ of maximal variation with klt general fiber and relative dimension $n$ there exist the following bounds:\n  1) a lower bound for the Chow-Mumford volume $\\left( \\lambda_{CM,f} \\right)^{\\dim T}$ of the form $\\delta^{\\dim T}$, where $\\delta$ is uniform;\n  2) a uniform lower bound on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.10515","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/2506.10515/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"}