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Finite jet determination of local CR automorphisms through resolution of degeneracies

Bernhard Lamel·Nordine Mir
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Abstract

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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Bernhard Lamel, Nordine Mir. 2006-09-14. Finite jet determination of local CR automorphisms through resolution of degeneracies. https://arxiv.org/abs/math/0609380

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