{"paper":{"title":"Key Varieties for Prime $\\mathbb{Q}$-Fano Threefolds Related with $\\mathbb{P}^{2}\\times\\mathbb{P}^{2}$-Fibrations. Part II","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hiromichi Takagi","submitted_at":"2021-11-29T05:08:56Z","abstract_excerpt":"We construct a $15$-dimensional affine variety $\\Pi_{\\mathbb{A}}^{15}$ with a ${\\rm GL}_{2}$- and $(\\mathbb{C}^{*})^{4}$-actions. We denote by $\\Pi_{\\mathbb{A}}^{14}$ the affine variety obtained from $\\Pi_{\\mathbb{A}}^{15}$ by setting one specified variable to $1$ (we refer the precise definition to Definition 1.1 of the paper). Let $\\Pi_{\\mathbb{P}}^{13}$ be several weighted projectivizations of $\\Pi_{\\mathbb{A}}^{14}$, and $\\Pi_{\\mathbb{P}}^{14}$ the weighted cone over $\\Pi_{\\mathbb{P}}^{13}$ with a weight one coordinate added. We show that $\\Pi_{\\mathbb{P}}^{13}$ or $\\Pi_{\\mathbb{P}}^{14}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.14328","kind":"arxiv","version":1},"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/2111.14328/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"}