{"paper":{"title":"The equivalence theory for infinite type hypersurfaces in $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Bernhard Lamel, Ilya Kossovskiy, Peter Ebenfelt","submitted_at":"2018-11-05T12:54:00Z","abstract_excerpt":"We develop a classification theory for real-analytic hypersurfaces in $\\mathbb C^2$ in the case when the hypersurface is of {\\em infinite type} at the reference point. This is the remaining, not yet understood case in $\\mathbb C^2$ in the {\\it Probl\\`eme local}, formulated by H.\\,Poincar\\'e in 1907 and asking for a complete biholomorphic classification of real hypersurfaces in complex space. One novel aspect of our results, appearing in this revised version, is a notion of {\\em smooth normal forms} for real-analytic hypersurfaces. We rely fundamentally on the recently developed CR -- DS techni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01649","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":""},"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"}