Parametrization of local biholomorphisms of real analytic hypersurfaces

Details Parametrization of local biholomorphisms of real analytic hypersurfaces Parametrization of local biholomorphisms of real analytic hypersurfaces

1997-04-25

arxiv.org/abs/math/9701201v1

Mathematics

Complex Variables

Scientific paper

Let $M$ be a real analytic hypersurface in $\bC^N$ which is finitely nondegenerate, a notion that can be viewed as a generalization of Levi nondegenerate, at $p_0\in M$. We show that if $M'$ is another such hypersurface and $p'_0\in M'$, then the set of germs at $p_0$ of biholomorphisms $H$ with $H(M)\subset M'$ and $H(p_0)=p'_0$, equipped with its natural topology, can be naturally embedded as a real analytic submanifold in the complex jet group of $\bC^N$ of the appropriate order. We also show that this submanifold is defined by equations that can be explicitly computed from defining equations of $M$ and $M'$. Thus, $(M,p_0)$ and $(M',p'_0)$ are biholomorphically equivalent if and only if this (infinite) set of equations in the complex jet group has a solution. Another result obtained in this paper is that any invertible formal map $H$ that transforms $(M,p_0)$ to $(M',p'_0)$ is convergent. As a consequence, $(M,p_0)$ and $(M',p'_0)$ are biholomorphically equivalent if and only if they are formally equivalent.

Affiliated with

Also associated with

No associations

Rating

Parametrization of local biholomorphisms of real analytic hypersurfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Parametrization of local biholomorphisms of real analytic hypersurfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Parametrization of local biholomorphisms of real analytic hypersurfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-679293