{"paper":{"title":"Divisorial Extractions from Singular Curves in Smooth 3-Folds, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Tom Ducat","submitted_at":"2014-03-29T10:09:29Z","abstract_excerpt":"Consider a singular curve $\\Gamma$ contained in a smooth 3-fold $X$. Assuming the general elephant conjecture, the general hypersurface section $\\Gamma\\subset S\\subset X$ is Du Val. Under that assumption, this paper describes the construction of a divisorial extraction from $\\Gamma$ by Kustin--Miller unprojection. Terminal extractions from $\\Gamma\\subset X$ are proved not to exist if $S$ is of type $D_{2k}, E_7$ or $E_8$ and are classified if $S$ is of type $A_1,A_2$ or $E_6$. The $A_n$ and $D_{2k+1}$ cases shall be considered in a further paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7614","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":""},"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"}