{"paper":{"title":"Algebraic approximation in CR geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Nordine Mir","submitted_at":"2012-02-11T19:53:51Z","abstract_excerpt":"We prove the following CR version of Artin's approximation theorem for holomorphic mappings between real-algebraic sets in complex space. Let $M\\subset \\C^N$ be a real-algebraic CR submanifold whose CR orbits are all of the same dimension. Then for every point $p\\in M$, for every real-algebraic subset $S'\\subset \\C^N\\times\\C^{N'}$ and every positive integer $\\ell$, if $f\\colon (\\C^N,p)\\to \\C^{N'}$ is a germ of a holomorphic map such that ${\\rm Graph}\\, f \\cap (M\\times \\C^{N'})\\subset S'$, then there exists a germ of a complex-algebraic map $f^\\ell \\colon (\\C^N,p)\\to \\C^{N'}$ such that ${\\rm Gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2463","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"}