{"paper":{"title":"Key varieties for prime $\\mathbb{Q}$-Fano threefolds defined by Jordan algebras of cubic forms. Part II","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Hiromichi Takagi","submitted_at":"2024-03-24T03:02:58Z","abstract_excerpt":"Subsequent to the previous paper [Tak5], we are concerned with the classification of complex prime $\\mathbb{Q}$-Fano $3$-folds of anti-canonical codimension 4 which are produced, as weighted complete intersections of appropriate weighted projectivizations of certain affine varieties related with $\\mathbb{P}^{2}\\times\\mathbb{P}^{2}$-fibrations. Such affine varieties or their appropriate weighted projectivizations (possibly allowing some coordinates have weights $0$) are called key varieties for prime $\\mathbb{Q}$-Fano 3-folds.\n  The purpose of this paper is to give new constructions of a $14$-d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.15991","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/2403.15991/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"}