{"paper":{"title":"On the CR transversality of holomorphic maps into hyperquadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Xiaojun Huang, Yuan Zhang","submitted_at":"2014-10-15T16:32:10Z","abstract_excerpt":"Let $M_\\ell$ be a smooth Levi-nondegenerate hypersurface of signature $\\ell$ in $\\mathbf C^n$ with $ n\\ge 3$, and write $H_\\ell^N$ for the standard hyperquadric of the same signature in $\\mathbf C^N$ with $N-n< \\frac{n-1}{2}$. Let $F$ be a holomorphic map sending $M_\\ell$ into $H_\\ell^N$. Assume $F$ does not send a neighborhood of $M_\\ell$ in $\\mathbf C^n$ into $H_\\ell^N$. We show that $F$ is necessarily CR transversal to $M_\\ell$ at any point. Equivalently, we show that $F$ is a local CR embedding from $M_\\ell$ into $H_\\ell^N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4116","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"}