Diederich-Fornaess theorem
DiederichFornaessTheorem
2007-12-05 14:07:28
2007-12-05 14:07:28
Theorem
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\begin{thm}[Diederich-Fornaes]
Let $X \subset {\mathbb{C}}^n$ be a compact real analytic subvariety. Then $X$ contains
no germ of a nontrivial complex analytic subvariety.
\end{thm}
In particular, all compact real analytic subvarieties (or submanifolds) are D'Angelo finite type at every point.
\begin{thebibliography}{9}
\bibitem{ber:submanifold}
M.\@ Salah Baouendi,
Peter Ebenfelt,
Linda Preiss Rothschild.
{\em \PMlinkescapetext{Real Submanifolds in Complex Space and Their Mappings}},
Princeton University Press,
Princeton, New Jersey, 1999.
\bibitem{DAngelo}
D'Angelo, John~P.
{\em \PMlinkescapetext{Several complex variables and the geometry of real
hypersurfaces}},
CRC Press, 1993.
\bibitem{DF}
Klas Diederich,
John E.\@ Fornaess.
{\em \PMlinkescapetext{Pseudoconvex domains with real-analytic boundary.}}
Ann. Math. (2) {\bf 107} (1978), no. 2, 371--384.
\end{thebibliography}