{"paper":{"title":"Threefold extremal contractions of type (IIA), I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shigefumi Mori, Yuri Prokhorov","submitted_at":"2016-01-28T07:19:26Z","abstract_excerpt":"Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f: (X, C)\\to (Z, o)$ such that $C=f^{-1}(o)_{red}$ and $-K_X$ is ample. Assume that $(X, C)$ contains a point of type (IIA) and that a general member $H\\in |O_X|$ containing $C$ is normal. We classify such germs in terms of $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07671","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":""},"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"}