{"paper":{"title":"On the boundedness of anti-canonical volumes of singular Fano $3$-folds in characteristic $p>5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Omprokash Das","submitted_at":"2018-08-06T20:41:56Z","abstract_excerpt":"In this article we prove the following version of the Weak-BAB conjecture for $3$-folds in char $p>5$: Fix a DCC set $I\\subset [0, 1)$ and an algebraically closed field $k$ of characteristic $p>5$. Let $\\mathfrak{D}$ be a collection of klt pairs $(X, \\Delta)$ satisfying the following properties: (1) $X$ is a projective $3$-fold, (2) $\\Delta$ is an $\\mathbb{R}$-divisor with coefficients in $I$, (3) $K_X+\\Delta\\equiv 0$, and (4) $-K_X$ is ample. Then the set $\\{\\mbox{vol}_X(-K_X) \\ | \\ (X, \\Delta)\\in\\mathfrak{D}\\mbox{ for some }\\Delta\\}$ is bounded from above."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02102","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}