{"paper":{"title":"Thom isotopy theorem for non proper maps and computation of sets of stratified generalized critical values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Si Tiep Dinh, Zbigniew Jelonek","submitted_at":"2018-05-07T18:19:01Z","abstract_excerpt":"Let $X\\subset\\Bbb C^n$ be an affine variety and $f:X\\to\\Bbb C^m$ be the restriction to $X$ of a polynomial map $\\Bbb C^n\\to\\Bbb C^m$. In this paper, we construct an affine Whitney stratification of $X$. The set $K(f)$ of stratified generalized critical values of $f$ can be also computed. We show that $K(f)$ is a nowhere dense subset of $\\Bbb C^m$, which contains the set $B(f)$ of bifurcation values of $f$ by proving a version of the isotopy lemma for non-proper polynomial maps on singular varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02681","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"}