Let $M \subset {\mathbb{C}}^n$ be a real analytic submanifold of real codimension 1. We say $M$ is of finite type in the sense of D'Angelo if there does not exist any germ of a complex analytic subvariety at $p \in M$ , that is contained in $M$ .

The Diederich-Fornaess theorem can be then restated to say that every compact real analytic subvariety of ${\mathbb{C}}^n$ is of D'Angelo finite type at every point.

Bibliography

1

M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. Real Submanifolds in Complex Space and Their Mappings, Princeton University Press, Princeton, New Jersey, 1999.

2

D'Angelo, John P. Several complex variables and the geometry of real hypersurfaces, CRC Press, 1993.