Non-embeddable real algebraic hypersurfaces (Q2435099)

The authors prove a series of results on non-embeddability of real algebraic hypersurfaces into special higher dimensional hypersurfaces. In particular, they present a compact strongly pseudoconvex hypersurface that does not admit a non-trivial holomorphic embedding into any Levi-nondegenerate real algebraic hypersurface in \(\mathbb C^N\) (Theorem 2.1). Other results concern local non-embeddability of real algebraic hypersurfaces with large Levi-degenerate sets into strongly pseudoconvex real algebraic hypersurfaces (Theorem 2.4) and the local non-embeddability of minimal real algebraic hypersurfaces with the Kohn-Nirenberg property into compact algebraic subsets admitting local holomorphic supporting functions (Theorem 3.6). Finally the authors present a family of real algebraic Levi-nondegenerate hypersurfaces of positive signature that cannot be embedded into a higher dimensional hyperquadric of the same signature.