{"paper":{"title":"Key Varieties for Prime $\\mathbb{Q}$-Fano Threefolds related with $\\mathbb{P}^2\\times \\mathbb{P}^2$-Fibrations. Part I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hiromichi Takagi","submitted_at":"2021-03-20T03:32:34Z","abstract_excerpt":"We construct a $14$-dimensional affine variety $\\Sigma^{14}_{\\mathbb{A}}$ with a $\\rm{GL}_3$- and a $(\\mathbb{C}^*)^6$-actions. We denote by $\\Sigma^{13}_{\\mathbb{A}}$ the affine variety obtained from $\\Sigma^{14}_{\\mathbb{A}}$ by setting one specified variable to $1$ (we refer the precise definition to Definition 1.1 of the paper). We show that several weighted projectivizations of $\\Sigma^{13}_{\\mathbb{A}}$ and $\\Sigma^{14}_{\\mathbb{A}}$ produce, as weighted complete intersections, examples of prime $\\mathbb{Q}$-Fano threefolds of codimension four belonging to $24$ classes of the graded ring"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.11086","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/2103.11086/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"}