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

Abstract

We show that there are strictly pseudoconvex, real algebraic hypersurfaces in \bC^{n+1} that cannot be locally embedded into a sphere in \bC^{N+1} for any $N$. In fact, we show that there are strictly pseudoconvex, real algebraic hypersurfaces in \bC^{n+1} that cannot be locally embedded into any compact, strictly pseudoconvex, real algebraic hypersurface