{"paper":{"title":"Cancellation for surfaces revisited. II","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":"2018-01-07T23:41:12Z","abstract_excerpt":"Let $X$ and $X'$ be affine algebraic varieties over a field $\\mathbb{k}$. The celebrated Zariski Cancellation Problem asks as to when the existence of an isomorphism $X\\times\\mathbb{A}^n\\cong X'\\times\\mathbb{A}^n$ implies $X\\cong X'$. In Part I of this paper (arXiv:1610.01805) we provided a criterion for cancellation in the case where $X$ is a normal affine surface admitting an $\\mathbb{A}^1$-fibration $X\\to B$ over a smooth affine curve $B$. If $X$ does not admit such an $\\mathbb{A}^1$-fibration then the cancellation by the affine line is known to hold for $X$ by a result of Bandman and Makar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02274","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"}