### Abstract

Let M ⊂ ℂ^{N} be a connected real-analytic hypersurface Levi form is nondegenerate at some point. We prove that for every point p ∈ M, there exists an integer k = k(M,p) such that germs at p of local realoanalytic CR automorphisms of M are uniquely determined by their k-jets (ar p). To prove this result we develop a new technique that can be seen as a resolution of the degeneracies of M. This procedure consists of blowing up M near an arbitrary point p ∈ M regardless of its minimality or nonminimality; then, thanks to the blow-up, the original problem can be reduced to an analogous one for a very special class of nonminimal hypersurfaces for which one may use known techniques to prove the finite jet determination property of its CR automorphisms.

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

Pages (from-to) | 201-216 |

Number of pages | 16 |

Journal | Asian Journal of Mathematics |

Volume | 11 |

Issue number | 2 |

Publication status | Published - Jun 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Blow-up
- CR automorphism
- Finite jet determination
- Nonminimal hypersurface

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Asian Journal of Mathematics*,

*11*(2), 201-216.

**Finite jet determination of local CR automorphisms through resolution of degeneracies.** / Lamel, Bernhard; Mir, Nordine.

Research output: Contribution to journal › Article

*Asian Journal of Mathematics*, vol. 11, no. 2, pp. 201-216.

}

TY - JOUR

T1 - Finite jet determination of local CR automorphisms through resolution of degeneracies

AU - Lamel, Bernhard

AU - Mir, Nordine

PY - 2007/6

Y1 - 2007/6

N2 - Let M ⊂ ℂN be a connected real-analytic hypersurface Levi form is nondegenerate at some point. We prove that for every point p ∈ M, there exists an integer k = k(M,p) such that germs at p of local realoanalytic CR automorphisms of M are uniquely determined by their k-jets (ar p). To prove this result we develop a new technique that can be seen as a resolution of the degeneracies of M. This procedure consists of blowing up M near an arbitrary point p ∈ M regardless of its minimality or nonminimality; then, thanks to the blow-up, the original problem can be reduced to an analogous one for a very special class of nonminimal hypersurfaces for which one may use known techniques to prove the finite jet determination property of its CR automorphisms.

AB - Let M ⊂ ℂN be a connected real-analytic hypersurface Levi form is nondegenerate at some point. We prove that for every point p ∈ M, there exists an integer k = k(M,p) such that germs at p of local realoanalytic CR automorphisms of M are uniquely determined by their k-jets (ar p). To prove this result we develop a new technique that can be seen as a resolution of the degeneracies of M. This procedure consists of blowing up M near an arbitrary point p ∈ M regardless of its minimality or nonminimality; then, thanks to the blow-up, the original problem can be reduced to an analogous one for a very special class of nonminimal hypersurfaces for which one may use known techniques to prove the finite jet determination property of its CR automorphisms.

KW - Blow-up

KW - CR automorphism

KW - Finite jet determination

KW - Nonminimal hypersurface

UR - http://www.scopus.com/inward/record.url?scp=34548258123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548258123&partnerID=8YFLogxK

M3 - Article

VL - 11

SP - 201

EP - 216

JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

SN - 1093-6106

IS - 2

ER -