Formal biholomorphic maps of real analytic hypersurfaces

Details Formal biholomorphic maps of real analytic hypersurfaces Formal biholomorphic maps of real analytic hypersurfaces

2000-02-28

arxiv.org/abs/math/0002235v2

Math. Res. Lett., vol. 7, p. 343-359, 2000

Mathematics

Complex Variables

15 pages, Latex

Scientific paper

Let f : (M,p)\to (M',p') be a formal biholomorphic mapping between two germs of real analytic hypersurfaces in \C^n, p'=f(p). Assuming the source manifold to be minimal at p, we prove the convergence of the so-called reflection function associated to f. As a consequence, we derive the convergence of formal biholomorphisms between real analytic minimal holomorphically nondegenerate hypersurfaces. Related results on partial convergence of formal biholomorphisms are also obtained.

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