{"paper":{"title":"Analytic Differential Equations and Spherical Real Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Ilya Kossovskiy, Rasul Shafikov","submitted_at":"2014-01-19T19:42:38Z","abstract_excerpt":"We establish an injective correspondence $M\\longrightarrow\\mathcal E(M)$ between real-analytic nonminimal hypersurfaces $M\\subset\\mathbb{C}^{2}$, spherical at a generic point, and a class of second order complex ODEs with a meromorphic singularity. We apply this result to the proof of the bound $\\mbox{dim}\\,\\mathfrak{hol}(M,p)\\leq 5$ for the infinitesimal automorphism algebra of an \\it arbitrary \\rm germ $(M,p)\\not\\sim(S^3,p')$ of a real-analytic Levi nonflat hypersurface $M\\subset\\mathbb{C}^2$ (the Dimension Conjecture). This bound gives the first proof of the dimension gap $\\mbox{dim}\\,\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4724","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"}