{"paper":{"title":"Algebraicity of holomorphic mappings between real algebraic sets in ${\\bold C}^n$","license":"","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Linda Preiss Rothschild, M. S. Baouendi, P. Ebenfelt","submitted_at":"1995-11-28T23:49:58Z","abstract_excerpt":"We give conditions under which a germ of a holomorphic mapping in $\\Bbb C^N$, mapping an irreducible real algebraic set into another of the same dimension, is actually algebraic.\n  Let $A\\subset \\bC^N$ be an irreducible real algebraic set.  Assume that there exists $\\po \\in A$ such that $A$ is a minimal, generic, holomorphically nondegenerate submanifold at $\\po$.  We show here that if $H$ is a germ at $p_1 \\in A$ of a holomorphic mapping from $\\bC^N$ into itself, with Jacobian $H$ not identically $0$, and $H(A)$ contained in a real algebraic set of the same dimension as $A$, then $H$ must ext"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9510201","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"}