{"paper":{"title":"Non-embeddability into a fixed sphere for a family of compact real algebraic hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ming Xiao, Xiaojun Huang, Xiaoshan Li","submitted_at":"2014-05-05T04:40:52Z","abstract_excerpt":"We study the holomorphic embedding problem from a compact strongly pseudoconvex real algebraic hypersurface into a sphere of higher dimension. We construct a family of compact strongly pseudoconvex hypersurfaces $M_{\\epsilon}$ in $\\mathbb{C}^2,$ and prove that for any integer $N$, there is a number $\\epsilon(N)$ with $0<\\epsilon(N)<1$ such that for any $\\epsilon$ with $0<\\epsilon<\\epsilon(N)$, $M_\\epsilon$ can not be locally holomorphically embedded into the unit sphere $\\mathbb{S}^{2N-1}$ in $\\mathbb{C}^N.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0778","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"}