Finite jet determination of local CR automorphisms through resolution of degeneracies

Bernhard Lamel, Nordine Mir

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)201-216
Number of pages16
JournalAsian Journal of Mathematics
Volume11
Issue number2
Publication statusPublished - Jun 2007
Externally publishedYes

    Fingerprint

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this