Obstructions to embeddability into hyperquadrics and explicit examples

Abstract

We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For this, we construct invariants attached to a given hypersurface that serve as obstructions to embeddability. We further study the embeddability problem for real-analytic submanifolds of higher codimension and answer a question by Forstnerič.

Revised version, appendix and references added

References in corpus (3)

• Most real analytic Cauchy-Riemann manifolds are nonalgebraizable
• Super-rigidity for CR embeddings of real hypersurfaces into hyperquadrics
• Transversality of holomorphic mappings between real hypersurfaces in different dimensions

Cited by in corpus (8)

• On the existence of holomorphic embeddings of strictly pseudoconvex algebraic hypersurfaces into spheres
• Flatness of CR Submanifolds in a Sphere
• Non-embeddable Real Algebraic Hypersurfaces
• CR and Holomorphic Embeddings and Pseudo-conformally Flat Metrics
• On the embeddability of real hypersurfaces into hyperquadrics
• Local orthogonal maps and rigidity of holomorphic mappings between real hyperquadrics
• Convergent normal form and canonical connection for hypersurfaces of finite type in ${\mathbb{C}}^2$
• Non-embeddability into a fixed sphere for a family of compact real algebraic hypersurfaces