{"paper":{"title":"A note on the stable equivalence problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pierre-Marie Poloni","submitted_at":"2013-08-12T19:20:34Z","abstract_excerpt":"We provide counterexamples to the stable equivalence problem in every dimension $d\\geq2$. That means that we construct hypersurfaces $H_1, H_2\\subset\\mathbb{C}^{d+1}$ whose cylinders $H_1\\times\\mathbb{C}$ and $H_2\\times\\mathbb{C}$ are equivalent hypersurfaces in $\\mathbb{C}^{d+2}$, although $H_1$ and $H_2$ themselves are not equivalent by an automorphism of $\\mathbb{C}^{d+1}$. We also give, for every $d\\geq2$, examples of two non-isomorphic algebraic varieties of dimension $d$ which are biholomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2652","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"}