Finite Jet Determination of Local CR Automorphisms through Resolution of Degeneracies

Let M 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. 2007 International Press.

Finite Jet Determination of Local CR Automorphisms through Resolution of Degeneracies Academic Article