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

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 $M_{\epsilon }$ 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 ${\mathbb{C}}^N.$

13 pages

References in corpus (1)

• On the existence of holomorphic embeddings of strictly pseudoconvex algebraic hypersurfaces into spheres