%0 Journal Article
%T Non-embeddability into a fixed sphere for a family of compact real algebraic hypersurfaces
%A Xiaojun Huang
%A Xiaoshan Li
%A Ming Xiao
%J Mathematics
%D 2014
%I arXiv
%X 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 $\mathbb{C}^N.$
%U http://arxiv.org/abs/1405.0778v1