{"paper":{"title":"On finite polynomial mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zbigniew Jelonek","submitted_at":"2018-07-15T14:52:22Z","abstract_excerpt":"Let $X\\subset \\mathbb{C}^n$ be a smooth irreducible affine variety of dimension $k$ and let $F: X\\to  \\mathbb{C}^m$ be a polynomial mapping. We prove that if $m\\ge k$, then there is a Zariski open dense subset $U$ in the space of linear mappings ${\\mathcal L}( \\mathbb{C}^n, \\mathbb{C}^m)$ such that for every $L\\in U$ the mapping $F+L$ is a finite mapping. Moreover, we can choose $U$ in this way, that all mappings $F+L; L\\in U$ are topologically equivalent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05558","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"}