{"paper":{"title":"An example of a compact non-C-analytic real subvariety of ${\\mathbb R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jiri Lebl","submitted_at":"2014-12-15T23:43:40Z","abstract_excerpt":"The purpose of this short expository note is to provide an example exhibiting some of the pathological properties of real-analytic subvarieties, where the pathology can be visualized, and the proofs use only elementary properties of analytic functions. We construct a compact irreducible real-analytic subvariety $S$ of ${\\mathbb R}^3$ of pure dimension two such that 1) the only a real-analytic function is defined in a neighbourhood of $S$ and vanishing on $S$ is the zero function, 2) the singular set of $S$ is not a subvariety of $S$, nor is it contained in any one-dimensional subvariety of $S$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4838","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1412.4838/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}