  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.

Complex Variables