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.

References in corpus (3)

• Obstructions to embeddability into hyperquadrics and explicit examples
• Most real analytic Cauchy-Riemann manifolds are nonalgebraizable
• Hermitian symmetric polynomials and CR complexity

Cited by in corpus (3)

• CR and Holomorphic Embeddings and Pseudo-conformally Flat Metrics
• Non-embeddability into a fixed sphere for a family of compact real algebraic hypersurfaces
• On the embeddability of real hypersurfaces into hyperquadrics