Finite jet determination of local CR automorphisms through resolution of degeneracies

Details Finite jet determination of local CR automorphisms through resolution of degeneracies Finite jet determination of local CR automorphisms through resolution of degeneracies

2006-09-14

arxiv.org/abs/math/0609380v1

Asian J. Math., 11(2), (2007), 201--216.

Mathematics

Complex Variables

16 pages

Scientific paper

Let M be a connected real-analytic hypersurface in N-dimensional complex euclidean space whose Levi form is nondegenerate at some point. We prove that for every point p in M, there exists an integer k=k(M,p) such that germs at p of local real-analytic CR automorphisms of M are uniquely determined by their k-jets (at 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 in 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.

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