{"paper":{"title":"Deformation equivalence of affine ruled surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hubert Flenner, Mikhail Zaidenberg, Shulim Kaliman","submitted_at":"2013-05-23T10:00:42Z","abstract_excerpt":"A smooth family $\\varphi:\\mathcal V\\to S$ of surfaces will be called {\\em completable} if there is a logarithmic deformation $(\\bar {\\mathcal V},{\\mathcal D})$ over $S$ so that ${\\mathcal V}=\\bar{\\mathcal V}\\backslash {\\mathcal D}$. Two smooth surfaces $V$ and $V'$ are said to be deformations of each other if there is a completable flat family ${\\mathcal V}\\to S$ of smooth surfaces over a connected base so that $V$ and $V'$ are fibers over suitable points $s,s'\\in S$. This relation generates an equivalence relation called {\\em deformation equivalence}. In this paper we give a complete combinat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5366","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"}