{"paper":{"title":"On finite regular and holomorphic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zbigniew Jelonek","submitted_at":"2014-04-29T19:19:44Z","abstract_excerpt":"Let $X, Y$ be smooth algebraic varieties of the same dimension. Let $f, g : X \\to Y$ be finite polynomial mappings. We say that $f, g$ are equivalent if there exists a regular automorphism $\\Phi \\in Aut(X)$ such that $f = g\\circ \\Phi$. Of course if $f, g$ are equivalent, then they have the same discriminant and the same geometric degree. We show, that conversely there is only a finite number of non-equivalent proper polynomial mappings $f : X \\to Y$, such that $D(f) = V$ and $\\mu(f) = k.$ We prove the same statement in the local holomorphic situation. In particular we show that if $f : (\\Bbb C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7466","kind":"arxiv","version":4},"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"}