# Diederich-Fornaess theorem

###### Theorem (Diederich-Fornaes).

Let $X\mathrm{\subset}{\mathrm{C}}^{n}$ be a compact real analytic subvariety. Then $X$ contains no germ of a nontrivial complex analytic subvariety.

In particular, all compact real analytic subvarieties (or submanifolds^{}) are D’Angelo finite type at every point.

## References

- 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
- 2 D’Angelo, John P. , CRC Press, 1993.
- 3 Klas Diederich, John E. Fornaess. Ann. Math. (2) 107 (1978), no. 2, 371–384.

Title | Diederich-Fornaess theorem |
---|---|

Canonical name | DiederichFornaessTheorem |

Date of creation | 2013-03-22 17:40:00 |

Last modified on | 2013-03-22 17:40:00 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 4 |

Author | jirka (4157) |

Entry type | Theorem |

Classification | msc 32V40 |

Classification | msc 32C07 |