{"paper":{"title":"Numerical characterization of the hard Lefschetz classes of dimension two, I: supercritical collections under certain rearrangement","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Jiajun Hu, Jian Xiao","submitted_at":"2023-09-10T12:00:17Z","abstract_excerpt":"We study the numerical characterization of two dimensional hard Lefschetz classes given by the complete intersections of nef classes. In Shenfeld and van Handel's breakthrough work on the characterization of the extremals of the Alexandrov-Fenchel inequality for convex polytopes, they proposed an open question on the algebraic analogue of the characterization. We settle the open question when the collection of nef classes is given by a rearrangement of supercriticality, which in particular includes the big nef collection as a special case.\n  The main results enable us to refine some previous r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05008","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/2309.05008/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"}