Non-embeddable Real Algebraic Hypersurfaces

TL;DR

This paper investigates classes of real hypersurfaces that cannot be embedded into more standard or symmetric hypersurfaces like spheres or algebraic ones, highlighting key obstructions and open problems.

Contribution

It identifies and analyzes conditions under which certain real hypersurfaces are non-embeddable into more symmetric or algebraic hypersurfaces, advancing understanding of their geometric properties.

Findings

Certain classes of hypersurfaces are proven non-embeddable into spheres or algebraic hypersurfaces.

The paper outlines open problems related to embeddability and classification of hypersurfaces.

Provides criteria and examples illustrating non-embeddability in complex geometry.

Abstract

We study various classes of real hypersurfaces that are not embeddable into more special hypersurfaces in higher dimension, such as spheres, real algebraic compact strongly pseudoconvex hypersurfaces or compact pseudoconvex hypersurfaces of finite type. We conclude by stating some open problems.