### Abstract

We consider (small) algebraic deformations of germs of realalgebraic Cauchy-Riemann submanifolds in complex space and study the biholomorphic equivalence problem for such deformations. We show that two algebraic deformations of minimal holomorphically nondegenerate real-algebraic CR submanifolds are holomorphically equivalent if and only if they are algebraically equivalent.

Original language | English |
---|---|

Pages (from-to) | 891-925 |

Number of pages | 35 |

Journal | Communications in Analysis and Geometry |

Volume | 18 |

Issue number | 5 |

Publication status | Published - Dec 2010 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistics and Probability
- Geometry and Topology
- Analysis
- Statistics, Probability and Uncertainty

### Cite this

**Holomorphic versus algebraic equivalence for deformations of real-algebraic Cauchy-Riemann manifolds.** / Lamel, Bernhard; Mir, Nordine.

Research output: Contribution to journal › Article

*Communications in Analysis and Geometry*, vol. 18, no. 5, pp. 891-925.

}

TY - JOUR

T1 - Holomorphic versus algebraic equivalence for deformations of real-algebraic Cauchy-Riemann manifolds

AU - Lamel, Bernhard

AU - Mir, Nordine

PY - 2010/12

Y1 - 2010/12

N2 - We consider (small) algebraic deformations of germs of realalgebraic Cauchy-Riemann submanifolds in complex space and study the biholomorphic equivalence problem for such deformations. We show that two algebraic deformations of minimal holomorphically nondegenerate real-algebraic CR submanifolds are holomorphically equivalent if and only if they are algebraically equivalent.

AB - We consider (small) algebraic deformations of germs of realalgebraic Cauchy-Riemann submanifolds in complex space and study the biholomorphic equivalence problem for such deformations. We show that two algebraic deformations of minimal holomorphically nondegenerate real-algebraic CR submanifolds are holomorphically equivalent if and only if they are algebraically equivalent.

UR - http://www.scopus.com/inward/record.url?scp=79957628819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957628819&partnerID=8YFLogxK

M3 - Article

VL - 18

SP - 891

EP - 925

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

SN - 1019-8385

IS - 5

ER -