Non-embeddability into a fixed sphere for a family of compact real algebraic hypersurfaces

2014/05/05 by Xiaojun Huang, Huang, Xiaojun, Xiaoshan Li +3
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1405.0778

13 pages

arxiv created 2014/05/05 · arxiv updated 2014/05/06

Abstract

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_ε in ℂ², and prove that for any integer N, there is a number ε(N) with 0<ε(N)<1 such that for any ε with 0<ε<ε(N), M_ε can not be locally holomorphically embedded into the unit sphere \mathbbS^2N-1 in ℂ^N.

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